Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33519 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
1144 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)(14,15)(16,17)(18,19)(20,29)(21,26)(22,34)(23,38)(24,27)(25,31)(28,36)(30,45)(32,46)(33,43)(35,40)(37,48)(39,44)(41,47)(42,49);(18,20)(19,25)(21,30)(22,35)(23,39)(24,32)(26,40)(27,41)(28,44)(29,34)(31,36)(33,47)(37,49)(38,42)(43,45)(46,48);(15,17)(18,21,24,23)(19,26,27,38)(20,30,32,39)(22,33,37,36)(25,40,41,42)(28,34,43,48)(29,45,46,44)(31,35,47,49);(19,27)(25,41)(26,38)(28,43)(29,46)(34,48)(40,42)(44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26507);