Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1284 |
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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)(5,8)(7,11)(9,10)(13,16,18,17);(2,3)(4,5)(6,10,11,8)(7,9)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^2,d^b=dg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1284, C2×#67682, #10684901, … |
| maximal normal subgroup of | D3×#1284, C2×#67682, #10684901, … |
| maximal quotient of | #10681718, #10681728, #10681735, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 258);