Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×C4×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ #534 |
| Sylow | C5 ⋊ #5653 |
| Sylow | C3 ⋊ #65987 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #534 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
692 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|d^2=f,c^a=cf,d^a=de,h^a=h^4,c^b=cf,d^b=def,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #14313245, #14425723, D5×#5653, … |
| maximal normal subgroup of | #14313245, #14425723, D5×#5653, … |
| maximal quotient of | #14322395, #14322416, #14322811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8864);