Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #1889 |
578 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 89 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 — 3 generators on 15 points:
(1,2,3)(8,10)(9,12)(11,15)(13,14);(2,3)(4,6,7,5)(8,9)(10,12)(11,13)(14,15);(4,5,7,6)(8,9)(10,14,15,12)(11,13)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,e^b=eg,h^b=h^2,d^c=dg,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10710943, #10710945, #10710985, … |
| maximal normal subgroup of | #10710943, #10710945, #10710985, … |
| maximal quotient of | #10689870, #10689880, #10690154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2598);