Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#4830 |
| Sylow | C3 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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)(14,16,17,21,18,15,19,20);(6,8,9,12)(7,10,11,13);(4,5)(6,7,9,11)(8,10,12,13)(14,15,17,20,18,16,19,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685749, #10685759, #10685955, … |
| maximal normal subgroup of | #10685749, #10685759, #10685955, … |
| maximal quotient of | C2×#68651, C2×#70465, C4×#4830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11581);