Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1280 |
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(4,5,6,7)(16,18)(17,20)(19,23)(21,22);(2,3)(8,9,10,12,11,13,14,15)(16,17)(18,22,23,20)(19,21)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=g,b^a=bc,c^a=cf,h^a=h^2,d^b=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #10681932, #10681933, #10681934, … |
| maximal normal subgroup of | #10681932, #10681933, #10681934, … |
| maximal quotient of | #10681717, #10681719, #10681725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 189);