Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C2×C13×#1789 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C2×C22⋊C4 |
| prime radical | C23×C13×#41 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C24×C4×C13 ◁ G | |
4102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27);(3,4)(5,6)(7,8,10,13,11,9,14,12);(7,9)(8,11)(10,12)(13,14);(4,6)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13592);