Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
712 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)(15,17)(20,28)(21,31)(22,33)(24,36)(26,41)(27,40)(29,46)(30,45)(32,35)(34,44)(37,48)(38,49)(39,47)(42,43);(14,15,16,17)(18,19)(20,24)(21,26)(22,27)(23,25)(28,36)(29,38)(30,37)(31,41)(32,42)(33,40)(34,39)(35,43)(44,47)(45,48)(46,49);(18,20,23,30)(19,24,25,37)(21,32,34,46)(22,35,33,29)(26,42,39,49)(27,43,40,38)(28,44,45,31)(36,47,48,41);(19,25)(24,37)(26,39)(27,40)(36,48)(38,43)(41,47)(42,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26575);