Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12981 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C23 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1869 |
| prime radical | C13×#525 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
488 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)(14,15,18,23,19,24,32,38,20,16,21,26,33,27,34,40)(17,25,29,37,30,39,42,45,28,22,31,35,41,36,43,44);(14,16,18,26,19,27,32,40,20,15,21,23,33,24,34,38)(17,25,31,35,30,39,43,44,28,22,29,37,41,36,42,45);(14,17)(15,22)(16,25)(18,31)(19,30)(20,28)(21,29)(23,37)(24,36)(26,35)(27,39)(32,43)(33,41)(34,42)(38,45)(40,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5969);