Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#427 ⋊ C2 |
| Sylow | C3 ⋊ #2948 |
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,15)(10,17)(13,16)(18,23);(2,3)(4,6,7,5)(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23);(2,3)(9,13)(11,19)(14,20)(15,16)(18,23)(21,22);(4,5,7,6)(8,9)(10,14)(11,13)(12,15)(16,19)(17,22)(18,20)(21,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^2,d^c=dg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10711302, #10711306, #10711811, … |
| maximal normal subgroup of | #10711302, #10711306, #10711811, … |
| maximal quotient of | #10764644, #10764857, #10765015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11743);