Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C103 ⋊ #1417 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 2 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)(104,106)(105,111)(107,124)(108,119)(109,131)(110,122)(112,138)(113,134)(114,143)(115,145)(116,136)(117,123)(118,127)(120,125)(121,129)(126,157)(128,159)(130,135)(132,150)(133,137)(139,151)(140,166)(141,165)(142,163)(144,167)(146,154)(147,156)(148,164)(149,162)(152,160)(153,155)(158,161);(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)(104,105,108,113,110,116,129,115)(106,117,119,146,122,147,121,153)(107,123,126,154,128,156,161,155)(109,130,125,114,132,142,160,144)(111,133,134,149,136,148,145,118)(112,137,139,162,141,164,140,127)(120,151,150,165,152,166,131,138)(124,143,157,163,159,167,158,135)Polycyclic presentation:
2^7,103|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^102,c^b=ce,e^b=ef,f^b=fg1160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2694);