Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62172 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3521 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,22,23,19)(17,25,26,20)(24,27,29,28)(30,31)(32,41)(33,45)(34,39)(35,40)(36,49)(37,44)(38,46)(42,57)(43,53)(47,54)(48,52)(50,55)(51,58)(56,60)(59,61);(14,16)(15,19)(17,24)(18,23)(20,27)(21,22)(25,28)(26,29)(30,32)(31,37)(33,42)(34,48)(35,44)(36,43)(38,51)(39,53)(40,41)(45,61)(46,60)(47,59)(49,52)(50,58)(54,57)(55,56);(30,33)(31,38)(32,42)(34,46)(35,47)(36,50)(37,51)(39,54)(40,55)(41,56)(43,58)(44,59)(45,49)(48,60)(52,61)(53,57);(16,23)(19,22)(24,29)(27,28)(30,34,35,36)(31,39,40,49)(32,43,44,48)(33,46,47,50)(37,52,41,53)(38,54,55,45)(42,58,59,60)(51,61,56,57);(14,17,18,26)(15,20,21,25)(16,24,23,29)(19,27,22,28)(31,40)(32,44)(38,55)(39,49)(42,59)(43,48)(45,54)(58,60)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55160);