Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #504×C103 ⋊ C2 |
| Sylow | C103 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 4 generators on 167 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(107,121)(112,135)(117,145)(122,149)(123,150)(132,158)(136,160)(137,154)(143,165)(146,157)(147,155)(151,164)(152,167)(153,161)(159,163)(162,166);(104,107)(105,112)(106,117)(108,122)(109,123)(110,121)(111,132)(113,136)(114,137)(115,135)(116,143)(118,146)(119,147)(120,145)(124,151)(125,152)(126,150)(127,153)(128,149)(129,154)(130,155)(131,157)(133,159)(134,158)(138,161)(139,162)(140,160)(141,163)(142,164)(144,165)(148,166)(156,167);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,106,110,120)(105,111,115,134)(107,117,121,145)(108,125,128,156)(109,130,126,119)(112,132,135,158)(113,139,140,148)(114,141,129,133)(116,142,144,124)(118,138,131,127)(122,152,149,167)(123,155,150,147)(136,162,160,166)(137,163,154,159)(143,164,165,151)(146,161,157,153);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105,110,115)(106,116,120,144)(107,112,121,135)(108,124,128,142)(109,129,126,114)(111,131,134,118)(113,138,140,127)(117,143,145,165)(119,148,130,139)(122,151,149,164)(123,154,150,137)(125,141,156,133)(132,157,158,146)(136,161,160,153)(147,166,155,162)(152,163,167,159)Polycyclic presentation:
2^7,103|a^2=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^102,e^b=ef,f^b=fg,h^b=h^102,d^c=dg2072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 17663);