Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#887 |
| Sylow | C3 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups; only the 941 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 941 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 5 generators on 19 points:
(1,2)(3,4)(5,6,7)(8,10,11,9)(14,18)(16,19);(12,14,15,18)(13,16,17,19);(6,7)(8,9,11,10)(12,13,15,17)(14,16,18,19);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686529, #10700614, #10700755, … |
| maximal normal subgroup of | #10686529, #10700614, #10700755, … |
| maximal quotient of | C22×#4649, C22×Dic3×C4⋊C4, C2×C4×#887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18276);