Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19010 |
| 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 | |
920 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)(16,24)(17,23)(18,22)(19,21)(20,25)(26,29)(27,28)(31,36)(33,34)(37,44)(38,41)(39,42)(43,45);(14,16)(15,20)(17,27)(18,25)(19,26)(21,28)(22,29)(23,24)(30,31)(32,37)(33,36)(34,41)(35,38)(39,43)(40,45)(42,44);(14,16)(15,20)(17,25)(18,27)(19,26)(21,28)(22,24)(23,29)(30,32)(31,37)(33,39)(34,42)(35,40)(36,43)(38,45)(41,44);(15,21)(20,28)(22,23)(24,29)(30,33,35,34)(31,36,38,41)(32,39,40,42)(37,43,45,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11998);