Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#500 ⋊ C2 |
| Sylow | C3 ⋊ #3175 |
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(4,6,7,10)(5,9,8,11)(13,18)(17,25)(19,24)(23,27);(12,14,21,26,16,22,15,20)(13,17,24,27,18,25,19,23);(2,3)(5,8)(9,11)(12,13)(14,17)(15,19)(16,18)(20,23)(21,24)(22,25)(26,27);(2,3)(4,5)(6,9)(7,8)(10,11)(14,20)(15,21)(17,23)(19,24)(22,26)(25,27)Polycyclic presentation:
2^7,3|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=dg,h^b=h^2,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10950300, #10950302, #10950345, … |
| maximal normal subgroup of | #10950300, #10950302, #10950345, … |
| maximal quotient of | #10795760, #10799454, #10799462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14511);