Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1282 |
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2)(4,6,8,11,9,10,7,5)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,7,10,9,11,8,6)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=g,e^2=g,b^a=bc,c^a=cf,h^a=h^2,d^b=df,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1282, C2×#67617, #10684837, … |
| maximal normal subgroup of | D3×#1282, C2×#67617, #10684837, … |
| maximal quotient of | #10681716, #10681728, #10681737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 193);