Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#819 |
| Sylow | C3 ⋊ C22×#108 |
480 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 309 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 — 4 generators on 23 points:
(5,6,7)(8,10,12,19,13,20,11,18)(9,14,15,17,16,22,21,23);(6,7)(8,9,11,15,13,16,12,21)(10,17,18,22,20,23,19,14);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10701071, #10701073, #10701076, … |
| maximal normal subgroup of | #10701071, #10701073, #10701076, … |
| maximal quotient of | C22×#4457, C22×#4458, C2×#69729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16311);