Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3165 |
380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,19);(12,13,14,16,15,17,18,19);(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^c=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10692696, #10692698, #10692733, … |
| maximal normal subgroup of | #10692696, #10692698, #10692733, … |
| maximal quotient of | #10795616, #10798577, #10799770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11082);