Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2139 |
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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 — 3 generators on 23 points:
(1,2,3)(9,14)(13,21)(15,20)(17,22);(8,9)(10,17)(11,20)(12,14)(13,16)(15,18)(19,22)(21,23);(2,3)(4,5,6,7)(9,13)(10,16)(11,18)(14,21)(15,22)(17,20)(19,23)Polycyclic presentation:
2^7,3|a^2=e,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,c^b=cg,d^b=df,f^b=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10710478, #10710483, #10710863, … |
| maximal normal subgroup of | #10710478, #10710483, #10710863, … |
| maximal quotient of | #10704932, #10705176, #10705228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4654);