Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ #3093 |
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 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)(17,25)(18,20)(24,26);(4,6,7,10)(5,9,8,11)(13,18)(15,23)(17,24)(19,20)(21,27)(25,26);(5,8)(9,11)(12,14,16,22)(13,17,19,25)(15,21,23,27)(18,24,20,26);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13)(14,17)(15,18)(16,19)(20,23)(21,24)(22,25)(26,27)Polycyclic presentation:
2^7,3|b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^2,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10828001, #10828004, #10828009, … |
| maximal normal subgroup of | #10828001, #10828004, #10828009, … |
| maximal quotient of | #10794991, #10795927, #10796422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14792);