Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33612 |
| 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 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
694 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)(19,24)(21,25)(22,32)(26,34)(27,35)(28,42)(30,38)(31,44)(33,39)(36,37)(40,49)(41,47)(43,48)(45,46);(18,19,25,37,22,28,33,35,23,27,39,42,32,36,21,24)(20,26,38,46,31,40,43,47,29,41,48,49,44,45,30,34);(15,17)(18,20)(19,26)(21,30)(22,31)(23,29)(24,34)(25,38)(27,41)(28,40)(32,44)(33,43)(35,47)(36,45)(37,46)(39,48)(42,49);(19,27)(20,29)(24,35)(28,36)(30,43)(31,44)(37,42)(38,48)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26600);