Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22890 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,24)(21,22)(25,32)(26,30)(27,33)(28,31);(14,16,17,15)(18,19)(20,27)(21,30)(22,24)(23,26)(25,28)(29,32)(31,33);(18,19)(20,25)(21,24)(22,30)(23,26)(27,28)(29,33)(31,32);(18,20)(19,25)(21,31)(22,28)(23,29)(24,32)(26,33)(27,30)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15878);