Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23492 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#120 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19)(20,24)(21,26)(22,30)(23,27)(25,28)(29,33)(31,32);(14,15)(16,17)(18,20)(19,24)(21,28)(22,31)(23,29)(25,26)(27,33)(30,32);(14,16,17,15)(18,20)(19,25)(21,28)(22,31)(23,29)(24,30)(26,33)(27,32);(18,21,23,22)(19,26,27,30)(20,28,29,31)(24,25,33,32)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16480);