Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×C3⋊C8 |
| Sylow | C3 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 333 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:
(4,5)(6,7,8,10,9,11,12,13);(1,2)(3,4,5)(14,16,17,21)(15,18,19,20);(14,15,17,19)(16,20,21,18);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×#101, #10685753, #10685762, … |
| maximal normal subgroup of | C3⋊C8×#101, #10685753, #10685762, … |
| maximal quotient of | C2×C4⋊C4×C3⋊C8, C4×Q8×C3⋊C8, C2×#69482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15008);