Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1790 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)(17,19)(18,22)(20,24)(21,26)(25,29)(27,28);(15,19)(17,26)(20,23)(21,22)(24,27)(28,29);(17,26)(19,21)(23,29)(24,27);(14,16)(15,20)(17,27)(18,25)(19,23)(21,29)(22,28)(24,26)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16860);