Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,20)(17,18)(19,21)(22,23)(24,34,39,49)(25,40)(26,30)(27,44)(28,33)(29,37,47,42)(31,35)(32,41)(36,46,51,53)(38,45,52,50)(43,48);(15,18)(19,20)(22,24,35,51,41,52,26,42,28,39,25,36,27,38,43,37)(23,29,30,45,44,53,31,49,33,47,48,50,32,46,40,34);(14,16,17,21)(15,19,18,20)(22,25,41,43,28,35,27,26)(23,30,44,31,33,48,32,40)(24,36,52,37,39,51,38,42)(29,45,53,49,47,50,46,34)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6276);