Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#942 |
| Fitting | C23×C3×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C22×#137 |
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:
(5,6,7)(8,11,12,21)(9,14,16,23)(10,17,18,20)(13,19,15,22);(1,2)(3,4)(8,10,12,18)(9,13,16,15)(11,20,21,17)(14,22,23,19);(6,7)(8,9)(10,13)(11,19)(12,16)(14,20)(15,18)(17,23)(21,22);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10701921, #10701925, #10701934, … |
| maximal normal subgroup of | #10701921, #10701925, #10701934, … |
| maximal quotient of | C22×#5225, C22×#4966, C22×#4964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19817);