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 ⋊ #2911 |
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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)(8,11,13,12)(9,15,16,21)(10,19,18,20)(14,17,22,23);(2,3)(10,18)(14,22)(17,23)(19,20);(8,10,12,20,13,18,11,19)(9,14,15,17,16,22,21,23);(4,5,6,7)(8,9)(10,17)(11,15)(12,21)(13,16)(14,20)(18,23)(19,22)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,d^2=g,e^2=g,b^a=be,e^a=eg,c^b=cg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10711706, #10711709, #10711757, … |
| maximal normal subgroup of | #10711706, #10711709, #10711757, … |
| maximal quotient of | #10764169, #10764208, #10764218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11753);