Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#4955 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#379 |
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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) = 96 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(7,9)(10,12,13,11)(15,17);(6,7)(8,9)(10,11)(12,13);(4,5)(14,15)(16,17);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10700447, #10700483, #10701504, … |
| maximal normal subgroup of | #10700447, #10700483, #10701504, … |
| maximal quotient of | C2×(C2×D3)⋊#95, C2×#71544, C4×#4955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14695);