Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #548 |
| Sylow | C5 ⋊ #5576 |
| Sylow | C3 ⋊ #65910 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C4×C5×Q8 | C2 |
| hypercenter | C4×Q8 | D15 |
| hypocenter | C3×C5 | #548 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
580 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 580 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.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,c^2=f,d^2=ef,d^a=de,g^a=g^2,h^a=h^4,c^b=cf165 conjugacy classes — view the full character table.
| maximal subgroup of | #14453435, #14453456, #14453493, … |
| maximal normal subgroup of | #14453435, #14453456, #14453493, … |
| maximal quotient of | Q8×#6714, #14326168, #14327277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10530);