Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,20)(19,21)(22,23,27,31)(24,32,35,47)(25,36,39,29)(26,40,42,30)(28,41,44,34)(33,49,37,48)(38,46,53,51)(43,50,45,52);(22,24,27,35)(23,28,31,44)(25,37,39,33)(26,41,42,34)(29,45,36,43)(30,47,40,32)(38,50,53,52)(46,48,51,49);(15,18)(16,21)(19,20)(22,25,26,38,27,39,42,53)(23,29,30,46,31,36,40,51)(24,33,34,50,35,37,41,52)(28,43,32,48,44,45,47,49)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3434);