Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C103 ⋊ #2222 |
140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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 — 3 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)(104,107)(105,113)(106,120)(108,126)(109,132)(110,127)(111,128)(112,134)(114,138)(115,142)(116,125)(117,139)(118,143)(119,148)(121,150)(122,154)(123,151)(124,152)(129,156)(130,159)(131,158)(133,160)(135,163)(136,155)(137,162)(140,164)(141,157)(144,166)(145,149)(146,165)(147,167)(153,161);(104,106,119,147,110,123,131,133,111,124,130,153,109,122,108,121)(105,112,129,145,116,136,141,146,117,137,140,144,115,135,114,118)(107,120,148,167,127,151,158,160,128,152,159,161,132,154,126,150)(113,134,156,149,125,155,157,165,139,162,164,166,142,163,138,143);(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)(104,105,111,117)(106,118,124,146)(107,125,128,142)(108,129,131,140)(109,116,110,115)(112,133,137,121)(113,132,139,127)(114,130,141,119)(120,149,152,166)(122,145,123,144)(126,157,158,138)(134,161,162,167)(135,153,136,147)(143,154,165,151)(148,156,159,164)(150,155,160,163)Polycyclic presentation:
2^7,103|a^2=g,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^102,e^c=eg2066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6635);