Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19048 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
908 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)(16,26)(17,28)(18,23)(19,24)(20,25)(21,27)(22,29)(31,35)(33,40)(36,44)(37,41)(38,42)(43,45);(14,16,20,17)(15,21,25,22)(18,29,19,27)(23,26,24,28)(30,31,34,37)(32,36,39,45)(33,41,40,35)(38,43,42,44);(14,17,20,16)(15,22,25,21)(18,29,19,27)(23,26,24,28)(30,32,34,39)(31,36,37,45)(33,42,40,38)(35,43,41,44);(14,18,20,19)(15,23,25,24)(16,27,17,29)(21,28,22,26)(31,37)(35,41)(36,45)(43,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12036);