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×#18763 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(30,31,35,38)(32,40,43,44)(33,36,34,39)(37,41,45,42);(14,16,19,25)(15,20,22,29)(17,24,18,27)(21,28,26,23)(31,36)(33,34)(37,44)(38,39)(40,45)(41,42);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(30,32,35,43)(31,37,38,45)(33,42,34,41)(36,44,39,40);(31,38)(36,39)(37,45)(40,44)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11751);