Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#4975 |
| Sylow | C3 ⋊ C2×#384 |
888 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 888 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) = 384 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9)(11,13)(15,17);(10,11,12,13);(4,5)(14,15,16,17);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10701004, #10701010, #10701030, … |
| maximal normal subgroup of | #10701004, #10701010, #10701030, … |
| maximal quotient of | C2×Dic3⋊#95, C2×#71563, C4×#4975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14722);