Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4914 |
| Fitting | C2×C3×SD32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#509 |
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,7,10,11)(8,15,17,21)(9,18,16,13)(12,20,19,14);(1,2)(7,12)(8,14)(9,16)(11,19)(13,21)(15,18)(17,20);(4,5)(7,11)(12,19)(13,18)(15,21);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10948502, C4×#4914, #10948524, … |
| maximal normal subgroup of | #10948502, C4×#4914, #10948524, … |
| maximal quotient of | C2×#69190, C2×#69221, C2×#69346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14598);