Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,27)(21,23)(22,26)(24,28)(25,31)(29,32)(30,33);(19,23)(21,31)(24,27)(25,26)(28,29)(32,33);(15,17)(18,19)(20,24)(21,25)(22,26)(23,31)(27,28)(29,33)(30,32);(18,20,22,30)(19,24,26,32)(21,29,31,28)(23,27,25,33)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16875);