Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4831 |
| Sylow | C3 ⋊ C2×#446 |
400 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 213 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) = 384 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(8,12)(10,13)(14,16,17,19,18,20,21,15);(6,8,9,12)(7,10,11,13);(4,5)(6,7,9,11)(8,10,12,13)(14,15,17,16,18,19,21,20);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10685771, #10685773, #10686011, … |
| maximal normal subgroup of | #10685771, #10685773, #10686011, … |
| maximal quotient of | C2×#68653, C2×#70466, C4×#4831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11582);