Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19063 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
806 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)(16,22)(17,24)(19,27)(20,25)(23,26)(28,29)(30,31)(32,42)(33,47)(34,39)(35,40)(36,41)(37,45)(38,49)(43,51)(44,52)(46,55)(48,53)(50,54)(56,58)(57,60)(59,61);(14,15,18,21)(16,19,23,28)(17,25,24,20)(22,29,26,27)(30,32)(31,37)(33,43)(34,44)(35,45)(36,46)(38,51)(39,42)(40,55)(41,52)(47,60)(48,57)(49,58)(50,59)(53,61)(54,56);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,24)(25,27)(30,33,36,50)(31,38,41,53)(32,43,46,59)(34,49,35,48)(37,51,52,61)(39,54,40,47)(42,56,55,60)(44,58,45,57);(30,34,36,35)(31,39,41,40)(32,44,46,45)(33,48,50,49)(37,42,52,55)(38,47,53,54)(43,57,59,58)(51,60,61,56)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12051);