Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,20,17,19)(22,23,28,33,26,31,27,32)(24,34,43,45,36,29,37,49)(25,38,42,30,40,48,41,47)(35,51,53,50,52,46,39,44);(14,16,18,17)(15,19,21,20)(22,24,26,36)(23,29,31,34)(25,39,40,53)(27,37,28,43)(30,46,47,51)(32,45,33,49)(35,41,52,42)(38,50,48,44);(22,25,26,40)(23,30,31,47)(24,35,36,52)(27,42,28,41)(29,44,34,50)(32,48,33,38)(37,53,43,39)(45,51,49,46);(14,17,18,16)(15,20,21,19)(23,31)(29,34)(30,47)(32,33)(38,48)(44,50)(45,49)(46,51)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17848);