Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62606 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
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)(16,23)(17,21)(18,27)(19,22)(20,25)(24,29)(26,28)(30,31)(32,41)(33,45)(34,39)(35,40)(36,50)(37,44)(38,48)(42,56)(43,53)(46,54)(47,60)(49,52)(51,61)(55,57)(58,59);(14,16)(15,20)(17,24)(18,26)(19,25)(21,28)(22,23)(27,29)(30,32)(31,37)(33,42)(34,49)(35,44)(36,43)(38,51)(39,53)(40,41)(45,59)(46,61)(47,58)(48,57)(50,52)(54,55)(56,60);(14,17,19,18)(15,21,22,27)(16,24,25,26)(20,28,23,29)(30,33,34,46,35,47,36,48)(31,38,50,60,40,54,39,45)(32,42,49,61,44,58,43,57)(37,51,52,56,41,55,53,59);(16,25)(20,23)(24,26)(28,29)(30,34,35,36)(31,39,40,50)(32,43,44,49)(33,46,47,48)(37,52,41,53)(38,45,54,60)(42,57,58,61)(51,56,55,59);(14,18,19,17)(15,21,22,27)(16,26,25,24)(20,28,23,29)(31,40)(32,44)(33,47)(39,50)(43,49)(46,48)(51,55)(56,59)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55594);