Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×D12 |
| Fitting | C2×C3×C4×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 17 points:
(3,4,5)(6,7,8,9);(1,2)(4,5)(7,9);(10,12,13,17)(11,14,15,16);(10,11,13,15)(12,16,17,14);(1,2)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10686913, #10686916, #10686929, … |
| maximal normal subgroup of | #10686913, #10686916, #10686929, … |
| maximal quotient of | C2×Q8×(C2×D3)⋊C4, C2×C4⋊C4×D12, C2×Q8×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18389);