Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#8415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #379 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#3515 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
704 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)(15,19,20,21)(22,23)(24,32,35,28)(25,36,38,45)(26,31)(27,30)(29,37,43,39)(33,48)(34,47,52,42)(40,44)(41,49)(46,51)(50,53);(14,15)(16,19)(17,21)(18,20)(22,24)(23,28)(25,33)(26,34)(27,35)(29,41)(30,32)(31,42)(36,53)(37,49)(38,50)(39,51)(40,52)(43,46)(44,47)(45,48);(14,16,18,17)(15,19,20,21)(22,25,27,38)(23,29,30,43)(24,33,35,50)(26,39,40,37)(28,41,32,46)(31,45,44,36)(34,51,52,49)(42,48,47,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1403);