Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7731 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C24×C13 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,20,21,18)(17,19)(22,23,25,27,26,24,28,29)(30,31)(32,39,41,44)(33,42)(34,37)(35,38)(36,40,45,43);(14,16,17,21)(15,18,19,20)(22,24)(23,26)(25,27)(28,29)(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42);(15,19)(18,20)(23,24)(27,29)(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 719);