Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33546 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| socle | C2×C13 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1236 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)(16,20)(17,19)(18,21)(22,25)(23,27)(24,26)(28,29);(15,19)(20,25)(21,26)(27,29);(17,24)(22,28);(14,16,18,23)(15,20,21,27)(17,22,24,28)(19,25,26,29)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26534);