Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3531 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
810 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)(16,23)(17,21)(18,26)(19,22)(20,24)(25,28)(27,29)(30,31,36,39)(32,42,45,54)(33,46,48,55)(34,41,35,40)(37,49,52,44)(38,50,53,47)(43,51,59,61)(56,57,60,58);(14,15)(16,20)(17,21)(18,26)(19,22)(23,27)(24,28)(25,29)(30,32,36,45)(31,37,39,52)(33,43,48,59)(34,49,35,44)(38,51,53,61)(40,54,41,42)(46,60,55,56)(47,58,50,57);(14,16)(15,20)(17,24)(18,27)(19,25)(21,28)(22,29)(23,26)(30,33)(31,38)(32,43)(34,47)(35,50)(36,48)(37,51)(39,53)(40,46)(41,55)(42,56)(44,57)(45,59)(49,58)(52,61)(54,60);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(31,39)(37,52)(38,53)(40,41)(42,54)(46,55)(51,61)(56,60)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12001);