Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19004 |
| 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 | |
896 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)(15,20)(16,24)(17,18)(22,23)(25,26)(27,28)(31,36)(33,34)(37,44)(38,41)(39,42)(43,45);(14,15)(16,21)(17,22)(18,20)(19,23)(24,28)(25,29)(26,27)(30,31,35,38)(32,37,40,45)(33,36,34,41)(39,43,42,44);(14,16)(15,21)(17,24)(18,26)(19,25)(20,27)(22,28)(23,29)(30,32)(31,37)(33,39)(34,42)(35,40)(36,43)(38,45)(41,44);(14,17,19,18)(15,22,23,20)(16,24,25,26)(21,28,29,27)(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, 11992);