Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C23×C3×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3003 |
994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 994 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) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,13)(12,14);(5,7);(9,12)(10,15)(13,14);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^7,3|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^2,e^b=eg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10693210, #10693216, #10767578, … |
| maximal normal subgroup of | #10693210, #10693216, #10767578, … |
| maximal quotient of | #10767557, #10767596, #10767635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16614);