Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13529 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,23)(20,24,25,22)(26,27,29,34,43,51,54,47,31,36,44,46,30,35,41,32)(28,37,38,52,45,57,56,49,40,53,55,48,39,50,42,33);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(27,32)(29,41)(30,43)(33,37)(34,35)(36,47)(38,42)(39,45)(44,54)(46,51)(48,57)(49,53)(50,52)(55,56);(15,17)(26,28,31,40)(27,33,36,49)(29,42,44,56)(30,45,43,39)(32,37,47,53)(34,50,46,57)(35,52,51,48)(38,54,55,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6517);