Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33802 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C23×C13 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 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)(32,36,41,51)(33,37,46,54)(34,47,45,39)(38,55,53,44)(42,52,56,48)(43,60,57,50)(49,58,61,59);(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)(37,52)(38,49)(39,50)(40,51)(44,59)(45,57)(46,56)(47,60)(48,54)(53,61)(55,58);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(31,37)(32,41)(33,44)(34,45)(36,48)(38,39)(40,54)(42,58)(46,55)(47,53)(49,60)(50,61)(51,52)(56,59);(15,21)(19,22)(20,29)(27,28)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26790);