Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#810 |
| Sylow | C3 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 — 3 generators on 19 points:
(1,2,3)(8,9,10,11)(13,16)(14,19)(17,18);(2,3)(12,13,15,18)(14,16,19,17);(4,5,6,7)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10685957, C8×#810, #10685971, … |
| maximal normal subgroup of | #10685957, C8×#810, #10685971, … |
| maximal quotient of | C4×#4484, #10685817, #10685822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2049);