Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×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 | |
578 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)(16,19)(17,18)(20,21)(22,23,29,35)(24,31,36,48)(25,30,39,45)(26,33,42,51)(27,32,43,50)(28,44,41,34)(37,49,52,47)(38,53,40,46);(15,18)(19,21)(22,24,27,37,28,38,42,39,29,36,43,52,41,40,26,25)(23,30,33,46,34,47,50,48,35,45,51,53,44,49,32,31);(14,16,17,20)(15,19,18,21)(22,25,26,40,41,52,43,36,29,39,42,38,28,37,27,24)(23,31,32,49,44,53,51,45,35,48,50,47,34,46,33,30);(24,36)(25,39)(30,45)(31,48)(37,52)(38,40)(46,53)(47,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26693);