Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1622 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)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31,35,40)(32,36,41,49)(33,38,44,52)(34,37,46,39)(42,48,54,59)(43,50,55,47)(45,51,57,53)(56,60,61,58);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,36)(33,42)(34,43)(35,41)(37,50)(38,48)(39,47)(40,49)(44,54)(45,56)(46,55)(51,60)(52,59)(53,58)(57,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(31,37)(32,41)(34,46)(36,47)(38,51)(39,40)(42,54)(45,57)(48,58)(49,50)(52,53)(59,60);(15,21)(19,22)(20,29)(27,28)(30,33)(31,38)(32,42)(34,45)(35,44)(36,48)(37,51)(39,53)(40,52)(41,54)(43,56)(46,57)(47,58)(49,59)(50,60)(55,61);(33,44)(38,52)(42,54)(45,57)(48,59)(51,53)(56,61)(58,60)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53872);