Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C2×C13×#2196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
1956 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(11,12,13,14,15,16,17,18,19,20,21,22,23);(3,4)(5,7)(6,8)(9,10);(4,7)(8,10);(5,9)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26531);