Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1032 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)(14,15,18,22,19,17,28,21)(16,23,26,24,27,29,25,20);(14,16,18,26,19,27,28,25)(15,20,22,23,17,24,21,29);(14,17)(15,19)(16,24)(18,22)(20,27)(21,28)(23,26)(25,29);(14,17)(15,19)(16,24)(18,21)(20,27)(22,28)(23,25)(26,29)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18184);