Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,24)(21,23)(22,25)(26,27,31,35)(28,32,37,46)(29,39,41,49)(30,42,44,34)(33,43,48,40)(36,50,51,57)(38,54,53,47)(45,55,56,52);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,36)(30,38)(31,37)(33,45)(34,47)(35,46)(39,50)(40,52)(41,51)(42,54)(43,55)(44,53)(48,56)(49,57);(15,17)(26,29,31,41)(27,33,35,48)(28,36,37,51)(30,43,44,40)(32,45,46,56)(34,49,42,39)(38,55,53,52)(47,57,54,50);(19,23)(22,24)(28,37)(32,46)(36,51)(38,53)(45,56)(47,54)(50,57)(52,55)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16931);