Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
454 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)(32,41)(33,38)(34,37)(35,48)(36,42)(39,47)(40,46)(43,49)(44,51)(45,53)(50,59)(52,57)(54,61)(55,60)(56,58);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,36)(33,42)(34,43)(35,44)(37,52)(38,41)(39,50)(40,51)(45,57)(46,58)(47,60)(48,56)(49,53)(54,55)(59,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(31,37)(32,42)(34,47)(35,46)(36,49)(38,53)(39,40)(41,52)(43,59)(45,61)(48,54)(50,56)(51,55)(57,60);(15,21)(19,22)(20,29)(27,28)(31,38)(32,42)(37,53)(39,54)(40,48)(43,57)(44,58)(59,60)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26798);