Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×#215 |
| Fitting | C2×C3×C4×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 — 4 generators on 17 points:
(1,2)(3,4,5)(10,11,13,15)(12,17,16,14);(4,5)(11,14)(12,16)(15,17);(1,2)(6,7,8,9);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10689745, #10689751, #10689767, … |
| maximal normal subgroup of | #10689745, #10689751, #10689767, … |
| maximal quotient of | C2×C8×#215, C2×#70933, C2×#70953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15000);