Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#29384 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2598 |
| prime radical | C13×#2010 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23)(17,20)(18,22)(19,24)(21,26)(25,28)(27,29);(14,16,17,24,18,25,26,29)(15,19,21,23,22,27,20,28);(19,27)(23,28);(15,20,22,21)(19,28,27,23)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22372);