Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#8862 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #385 |
| prime radical | C24×C13 | C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20)(16,18,21,19)(22,23,26,30,27,31,37,43)(24,28,34,40,33,39,47,51)(25,29,36,42,35,41,48,52)(32,44,46,53,45,38,49,50);(15,18)(16,21)(19,20)(22,24,26,34,27,33,37,47)(23,28,30,40,31,39,43,51)(25,32,36,46,35,45,48,49)(29,38,42,50,41,44,52,53);(22,25)(23,29)(24,32)(26,36)(27,35)(28,38)(30,42)(31,41)(33,45)(34,46)(37,48)(39,44)(40,50)(43,52)(47,49)(51,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1850);