Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17684 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3517 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24,20,23,18,22)(16,25,26,29,17,21,27,28)(30,31)(32,38,40,45)(33,37)(34,36)(35,39,43,41)(42,44);(14,16,20,17)(15,21,23,25)(18,26,19,27)(22,28,24,29)(30,32)(31,35)(33,41)(34,40)(36,43)(37,45)(38,44)(39,42);(14,17,20,16)(15,21,23,25)(18,26,19,27)(22,29,24,28)(31,36)(35,43)(37,44)(38,45);(14,18,20,19)(15,22,23,24)(16,26,17,27)(21,28,25,29)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10672);