Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32698 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
594 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)(14,15,19,22,18,23,27,29)(16,20,21,28,24,17,25,26);(14,16)(15,20)(17,23)(18,24)(19,25)(21,27)(22,26)(28,29);(14,17)(15,21,23,25)(16,22,24,29)(18,20)(19,26)(27,28);(16,24)(19,27)(22,29)(26,28)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25686);