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 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C61 | C4 |
| prime radical, cosocle | D3233 | 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:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,52)(36,50,51,60)(40,54,55,57)(44,58,59,53)(46,61,56,49)(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);(1,2,5,10,19,32,47,51,35,22,13,6,11,20,33,49,50,30,46,55,39,26,15,24,37,53,54,34,17,29,44,59,43,28,41,57,58,38,21,8,16,27,40,56,45,60,61,42,25,12,3,7,14,23,36,52,48,31,18,9,4)(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^50,c^b=c^52,d^b=d^60812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12932, 8);