Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18723 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3548 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ 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)(15,20)(17,18)(21,27)(22,26)(23,25)(28,29)(30,31,35,39)(32,40,43,44)(33,38,34,37)(36,41,45,42);(14,15,19,22)(16,21,24,29)(17,20,18,26)(23,28,25,27)(30,32,35,43)(31,36,39,45)(33,41,34,42)(37,44,38,40);(14,16)(15,21)(17,25)(18,23)(19,24)(20,27)(22,29)(26,28)(31,37)(33,34)(36,44)(38,39)(40,45)(41,42);(14,17,19,18)(15,20,22,26)(16,23,24,25)(21,28,29,27)(30,33,35,34)(31,37,39,38)(32,41,43,42)(36,44,45,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11711);