Finite Group DatabasebetaFinite Group Databasebeta| order | 12932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C53×C61 ⋊ C4 |
| Sylow | C61 ⋊ #6157 |
| Sylow | C53 ⋊ Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C61 | C4 |
| prime radical, cosocle | C61×D53 | C2 |
| LCS | G ▷ C53×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 114 |
| transitive degree | μt(G) = 3233 |
A minimal faithful permutation representation — 2 generators on 114 points:
(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)(63,64,65,67)(66,69,70,76)(68,73,74,72)(71,78,79,89)(75,82,83,85)(77,86,87,81)(80,91,92,104)(84,95,96,101)(88,93,99,98)(90,102,103,94)(97,105,106,111)(100,107,108,110)(109,112,113,114);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(62,63,66,71,80,93,82,69,77,88,100,109,112,105,91,103,89,101,110,106,96,83,74,67,72,81,94,102,86,73,64,68,75,84,97,107,95,78,90,104,111,114,113,108,99,87,76,85,98,92,79,70,65)Polycyclic presentation:
2^2,53,61|a^2=b,c^a=c^30,d^a=d^60,c^b=c^52857 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12932, 10);