Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#821 |
| Fitting | C23×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(5,6,7)(9,11)(12,13,14,16,15,17,18,19);(6,7)(8,9)(10,11)(13,16)(14,18)(17,19);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10700750, #10700754, #10701448, … |
| maximal normal subgroup of | #10700750, #10700754, #10701448, … |
| maximal quotient of | C22×#4459, C2×#70762, C2×#70758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16314);