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×#61077 |
| 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 | |
2762 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)(20,29)(21,28)(22,26)(23,25)(24,27)(30,33)(31,32);(18,20)(19,22)(21,26)(23,32)(24,30)(25,29)(27,31)(28,33);(15,17)(18,21,24,23)(19,25,27,28)(20,26,30,32)(22,29,31,33);(18,22,24,31)(19,26,27,32)(20,25,30,28)(21,29,23,33);(19,27)(20,30)(25,28)(26,32)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54065);