Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×#95 ⋊ C2 |
| Hall | C3×C5 ⋊ #396 |
| Sylow | C5 ⋊ #4676 |
| Sylow | C3 ⋊ #64965 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D15 |
| commutator, socle, cosocle | C23×C3×C5 | C23 |
| Fitting | C3×C5×#95 | C2 |
| prime radical | C23×D15 | C22 |
| hypercenter | #95 | D15 |
| hypocenter | C3×C5 | #396 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ #95 | |
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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=d,c^2=ef,b^a=be,c^a=cdef,g^a=g^2,h^a=h^4,c^b=cf162 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#396, C2×#11750777, D5×#4676, … |
| maximal normal subgroup of | D15×#396, C2×#11750777, D5×#4676, … |
| maximal quotient of | #14280056, #14280123, #14280216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4972);