Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33584 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
722 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)(18,19)(20,30)(21,29)(22,25)(23,36)(24,27)(26,33)(28,38)(31,47)(32,46)(34,41)(35,43)(37,45)(39,44)(40,48)(42,49);(14,15,16,17)(19,25)(26,40)(27,29)(28,41)(30,46)(36,43)(42,45)(44,47);(18,20)(19,26)(21,31)(22,32)(23,37)(24,39)(25,40)(27,42)(28,44)(29,45)(30,36)(33,38)(34,48)(35,49)(41,47)(43,46);(18,21,22,24)(19,27,25,29)(20,31,32,39)(23,34,35,38)(26,42,40,45)(28,43,41,36)(30,44,46,47)(33,37,48,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26572);