Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
870 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)(17,24)(19,25)(20,27)(22,28)(30,31,36,41)(32,42,45,55)(33,38,47,53)(34,40,35,39)(37,49,51,44)(43,56,59,60)(46,54,48,52)(50,57,61,58);(14,15)(16,19)(17,20)(18,21)(22,26)(23,25)(24,27)(28,29)(30,32,36,45)(31,37,41,51)(33,43,47,59)(34,44,35,49)(38,50,53,61)(39,42,40,55)(46,57,48,58)(52,60,54,56);(14,16)(15,19)(17,22)(18,23)(20,26)(21,25)(24,28)(27,29)(30,33)(31,38)(32,43)(34,48)(35,46)(36,47)(37,50)(39,54)(40,52)(41,53)(42,56)(44,58)(45,59)(49,57)(51,61)(55,60);(14,17,18,24)(15,20,21,27)(16,22,23,28)(19,26,25,29)(30,34,36,35)(31,39,41,40)(32,44,45,49)(33,46,47,48)(37,42,51,55)(38,52,53,54)(43,57,59,58)(50,60,61,56)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11453);