Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13164 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #121 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1939 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,24,35,42,21,26,34,23,18,36,17,33)(16,27,31,44,29,22,37,40,32,39,45,43,30,41,28,38);(14,16,19,31,20,29,35,37,21,32,34,45,18,30,17,28)(15,22,25,40,24,39,42,43,26,41,23,38,36,27,33,44);(14,17,18,34,21,35,20,19)(15,23,24,33,26,25,36,42)(16,28,30,45,32,37,29,31)(22,38,39,44,41,40,27,43)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6152);