Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #1020⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#1020⋊C2 |
| unambiguous semidirect product | #1020⋊C22 |
| Fitting | C2×#120 ⋊ D3 |
| derived | C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #1020⋊C2 |
| commutator, cosocle, hypocenter | C22⋊A4 | C23 |
| Frattini | C22 | C22×S4 |
| Fitting | C2×#120 | D3 |
| socle | C23 | C2×S4 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C2 | |
463 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 463 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 10 |
| transitive degree | μt(G) = 12 |
A minimal faithful permutation representation — 3 generators on 10 points:
(3,7,5,8,6,4)(9,10);(5,10)(7,8);(1,2)28 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17948);