Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C22×C13×#361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #102 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C23×C13×D8 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
1390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6,8,12,9,14,19,13)(7,15,17,11,18,10,16,20);(6,10)(7,16)(8,19)(11,12)(13,20)(14,15)(17,18)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26377);