Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
1640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 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)(30,31,36,40)(32,37,43,52)(33,45,47,53)(34,39,35,48)(38,49,54,46)(41,55,57,60)(42,51,44,58)(50,59,61,56);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32)(31,37)(33,41)(34,42)(35,44)(36,43)(38,50)(39,51)(40,52)(45,55)(46,56)(47,57)(48,58)(49,59)(53,60)(54,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33)(31,38)(32,41)(34,46)(35,49)(36,47)(37,50)(39,53)(40,54)(42,56)(43,57)(44,59)(45,48)(51,60)(52,61)(55,58);(15,21)(19,22)(20,29)(27,28)(30,34,36,35)(31,39,40,48)(32,42,43,44)(33,46,47,49)(37,51,52,58)(38,53,54,45)(41,56,57,59)(50,60,61,55);(32,43)(37,52)(41,57)(42,44)(50,61)(51,58)(55,60)(56,59)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53864);