Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63066 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7352 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,19)(16,17,20,21)(22,23)(24,32)(25,27)(26,30)(28,29)(31,35)(33,37)(34,36);(15,19)(16,20)(23,29)(25,35)(30,32)(33,36);(14,16)(15,17)(18,20)(19,21)(22,24,28,26)(23,30,29,32)(25,33,35,36)(27,34,31,37);(14,17)(15,16)(18,21)(19,20)(22,25)(23,31)(24,33)(26,36)(27,29)(28,35)(30,37)(32,34);(22,26,28,24)(23,30,29,32)(25,36,35,33)(27,34,31,37);(22,27,28,31)(23,25,29,35)(24,34,26,37)(30,33,32,36)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56054);