Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,24,28,25,29,23,39)(20,30,32,26,21,33,35,42)(22,36,37,27,38,43,40,44)(31,41,47,48,34,49,46,45);(14,15)(16,17)(18,20,24,32,25,21,23,35)(19,26,28,33,29,42,39,30)(22,31,37,47,38,34,40,46)(27,41,43,48,44,49,36,45);(15,17)(18,21)(19,26)(20,25)(22,34)(23,35)(24,32)(27,41)(28,30)(29,42)(31,38)(33,39)(36,48)(37,47)(40,46)(43,45)(44,49);(18,22,25,38)(19,27,29,44)(20,31,21,34)(23,40,24,37)(26,41,42,49)(28,43,39,36)(30,45,33,48)(32,47,35,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18177);