Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33373 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#99 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C2×Q8 | C24×C13 |
| prime radical | C13×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×Q8×C13 ◁ C2×C13×H(5,𝔽2) ◁ G | |
1312 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)(14,15,19,25,20,26,16,22)(17,23,28,21,18,24,27,29);(14,16,20,19)(15,21,26,29)(17,27,18,28)(22,24,25,23);(14,16,20,19)(15,22,26,25)(17,28,18,27)(21,24,29,23);(14,17,20,18)(15,23,26,24)(16,27,19,28)(21,22,29,25)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26361);