Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33500 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C23×C8 |
| prime radical | C23×C13 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
460 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)(30,31,33,37,34,38,43,49,35,39,44,50,45,51,55,59)(32,36,41,47,42,48,54,58,40,46,52,56,53,57,60,61);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,36)(33,41)(34,42)(35,40)(37,47)(38,48)(39,46)(43,54)(44,52)(45,53)(49,58)(50,56)(51,57)(55,60)(59,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(32,40)(36,46)(41,52)(42,53)(47,56)(48,57)(54,60)(58,61);(15,21)(19,22)(20,29)(27,28)(32,40)(36,46)(41,52)(42,53)(47,56)(48,57)(54,60)(58,61)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26488);