Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#4650 |
| Sylow | C3 ⋊ C2×#382 |
712 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 309 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:
(3,4,5)(6,7,8,9)(11,12)(14,16)(15,18)(17,20)(19,21);(1,2)(10,12,13,11)(14,15,17,19)(16,18,20,21);(4,5)(10,11,13,12)(16,20)(18,21);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10684801, #10685193, #10685229, … |
| maximal normal subgroup of | #10684801, #10685193, #10685229, … |
| maximal quotient of | C2×#69402, C2×#69401, C2×Dic3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5899);