Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#405 ⋊ C2 |
| Sylow | C3 ⋊ #3136 |
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(13,19)(17,24)(18,25)(23,27);(5,9)(8,11)(12,14,15,20,16,21,22,26)(13,18,17,23,19,25,24,27);(4,6,7,10)(5,8,9,11)(12,13,15,17,16,19,22,24)(14,18,20,23,21,25,26,27);(2,3)(4,5)(6,8)(7,9)(10,11)(13,17)(14,20)(15,22)(18,25)(19,24)(21,26)Polycyclic presentation:
2^7,3|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10865138, #10865142, #10865168, … |
| maximal normal subgroup of | #10865138, #10865142, #10865168, … |
| maximal quotient of | #10795396, #10797837, #10797855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11139);