Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1804 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
390 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)(14,15,17,23,20,25,19,37)(16,26,29,21,30,40,27,41)(18,32,31,38,36,45,35,24)(22,34,43,33,39,44,42,28);(14,16)(15,21,25,41)(17,27)(18,33)(19,29)(20,30)(22,38,39,24)(23,26,37,40)(28,36)(31,34)(32,42,45,43)(35,44);(14,16)(15,22)(17,29)(18,34)(19,27)(20,30)(21,38)(23,43)(24,41)(25,39)(26,32)(28,35)(31,33)(36,44)(37,42)(40,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5816);