Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | SD16×Dic6 |
| Sylow | C3 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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:
(1,2,3)(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8);(13,16)(14,19)(17,18);(12,13,15,18)(14,16,19,17)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10784680, #10784689, #10784740, … |
| maximal normal subgroup of | #10784680, #10784689, #10784740, … |
| maximal quotient of | Dic6×#102, Dic6×#103, SD16×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12207);