Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61074 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#525 ◁ G | |
2774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,28)(20,30,31,32)(21,29,23,26)(22,27,25,33);(18,20)(19,25)(21,27)(22,28)(23,33)(24,31)(26,30)(29,32);(15,17)(18,21,24,23)(19,26,28,29)(20,27,31,33)(22,32,25,30);(18,22)(19,27)(20,29)(21,32)(23,30)(24,25)(26,31)(28,33);(19,28)(20,31)(26,29)(27,33)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54062);