Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18765 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3482 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
902 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)(14,15,19,22)(16,23,25,28)(17,21,18,26)(20,27,29,24)(30,31,36,41)(32,38,43,44)(33,37,42,45)(34,40,35,39);(14,16)(15,20)(17,24)(18,27)(19,25)(21,28)(22,29)(23,26)(30,32,36,43)(31,37,41,45)(33,34,42,35)(38,39,44,40);(30,33)(31,38)(32,34)(35,43)(36,42)(37,39)(40,45)(41,44);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(30,34,36,35)(31,39,41,40)(32,42,43,33)(37,44,45,38)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11753);