Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3170 |
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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:
(1,2,3)(4,6,7,10)(5,9,8,11);(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20);(5,8)(9,11);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22)Polycyclic presentation:
2^7,3|a^2=g,c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10690428, #10690430, #10694341, … |
| maximal normal subgroup of | #10690428, #10690430, #10694341, … |
| maximal quotient of | #10795726, #10799414, #10800362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11051);