Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ #1821 |
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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 — 3 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(13,16)(14,18);(2,3)(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10705867, #10705871, #10705880, … |
| maximal normal subgroup of | #10705867, #10705871, #10705880, … |
| maximal quotient of | #10688509, #10688518, #10688524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1566);