Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#431 ⋊ C2 |
| Sylow | C3 ⋊ #2972 |
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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 — 4 generators on 19 points:
(1,2,3)(13,17)(16,18);(2,3)(14,19)(16,18);(2,3)(12,14)(13,16)(15,19)(17,18);(4,5,6,8,7,9,10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^2,h^c=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10689047, #10689050, #10689829, … |
| maximal normal subgroup of | #10689047, #10689050, #10689829, … |
| maximal quotient of | #10793858, #10793917, #10794071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11862);