Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×C3⋊C8 |
| Sylow | C3 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 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 — 3 generators on 19 points:
(2,3)(4,5,6,8,7,9,10,11);(1,2,3)(13,16)(17,19);(12,13,14,17,15,16,18,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685744, C3⋊C8×#100, #10685749, … |
| maximal normal subgroup of | #10685744, C3⋊C8×#100, #10685749, … |
| maximal quotient of | C3⋊C8×#97, #10684568, #10685612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2422);