Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(2,3)(4,5,6,7)(9,12)(13,14);(1,2,3)(8,9)(10,14,15,12)(11,13)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,b^a=bc,c^a=cf,f^a=fg,d^b=df,h^b=h^2,d^c=dg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1390, C2×#67694, #10710128, … |
| maximal normal subgroup of | D3×#1390, C2×#67694, #10710128, … |
| maximal quotient of | #10682145, #10682181, #10682186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 270);