Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C103 ⋊ #1401 |
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)(105,112)(107,123)(108,126)(109,121)(110,119)(111,122)(113,136)(114,139)(115,134)(116,118)(117,135)(120,129)(124,147)(125,151)(127,154)(128,132)(130,148)(131,150)(133,142)(137,145)(138,160)(140,162)(141,153)(143,146)(144,159)(149,156)(152,166)(155,157)(158,164)(161,165)(163,167);(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)(104,105,108,114,109,115,127,140,110,116,128,141,130,143,155,163,111,117,129,142,131,144,156,164,107,113,124,137,125,138,152,161)(106,118,120,145,121,146,149,165,119,135,147,139,148,159,166,162,122,136,126,153,150,160,154,167,123,112,132,133,151,134,157,158)Polycyclic presentation:
2^7,103|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^102,c^b=cg,d^b=dg2096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2652);