Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×D3×Q16 |
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ C23×Q16 |
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(3,4)(5,6,7)(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16);(1,2)(3,4)(8,9,12,15)(10,16,18,23)(11,19,21,14)(13,20,22,17);(6,7);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710831, #10710852, D3×#1878, … |
| maximal normal subgroup of | #10710831, #10710852, D3×#1878, … |
| maximal quotient of | C22×D3×#103, C22×D3×#107, C2×C4×D3×Q16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19754);