Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18443 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(17,18)(21,28)(22,26)(23,24)(27,29)(30,31,35,39)(32,40,43,53)(33,37,44,51)(34,46,48,38)(36,47,50,42)(41,54,55,61)(45,58,57,52)(49,59,60,56);(14,15,19,22)(16,21,25,29)(17,20,18,26)(23,28,24,27)(30,32,35,43)(31,36,39,50)(33,41,44,55)(34,47,48,42)(37,49,51,60)(38,53,46,40)(45,59,57,56)(52,61,58,54);(14,16,19,25)(15,21,22,29)(17,24,18,23)(20,27,26,28)(30,33,35,44)(31,37,39,51)(32,41,43,55)(34,45,48,57)(36,49,50,60)(38,52,46,58)(40,54,53,61)(42,56,47,59);(14,17,19,18)(15,20,22,26)(16,23,25,24)(21,28,29,27)(33,44)(37,51)(41,55)(45,57)(49,60)(52,58)(54,61)(56,59)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11431);