Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#476 ⋊ C2 |
| Sylow | C3 ⋊ #3116 |
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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)(12,15,17,16)(13,20,21,19)(14,22,24,23)(18,26,27,25);(13,19)(15,16)(18,25)(20,21)(22,23)(26,27);(2,3)(5,8)(9,11)(12,14,17,24)(13,18,21,27)(15,22,16,23)(19,25,20,26);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,17,21)(14,18,24,27)(15,20,16,19)(22,26,23,25)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,h^b=h^2,d^c=dg,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | #10771523, #10771527, #10771553, … |
| maximal normal subgroup of | #10771523, #10771527, #10771553, … |
| maximal quotient of | #10795267, #10798208, #10798240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13623);