Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#121 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1606 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)(30,31,35,39)(32,36,41,50)(33,43,45,53)(34,46,48,38)(37,47,52,44)(40,54,55,61)(42,58,57,51)(49,59,60,56);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,36)(33,40)(34,42)(35,41)(37,49)(38,51)(39,50)(43,54)(44,56)(45,55)(46,58)(47,59)(48,57)(52,60)(53,61);(30,33,35,45)(31,37,39,52)(32,40,41,55)(34,47,48,44)(36,49,50,60)(38,53,46,43)(42,59,57,56)(51,61,58,54);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(32,41)(36,50)(40,55)(42,57)(49,60)(51,58)(54,61)(56,59);(15,21)(19,22)(20,29)(27,28)(32,41)(36,50)(40,55)(42,57)(49,60)(51,58)(54,61)(56,59)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54854);