Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #1790 |
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(8,9)(10,12)(11,13)(14,15);(2,3)(8,10)(9,12)(11,15)(13,14);(2,3)(4,5,6,7)(8,9)(10,14,15,12)(11,13)Polycyclic presentation:
2^7,3|a^2=f,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,e^b=eg,f^b=fg,h^b=h^2,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10712445, #10712446, #10712452, … |
| maximal normal subgroup of | #10712445, #10712446, #10712452, … |
| maximal quotient of | #10686578, #10686581, #10686696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2609);