Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#131 ⋊ D3 |
| Sylow | C5 ⋊ #5405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×C5⋊S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C2×C4 |
| Fitting | C5×#131 | D3 |
| socle | C2×C5 | C4×S4 |
| prime radical | #91955 | C2 |
| cosocle | C5×#41⋊C3 | C22 |
| hypercenter | C8 | C5⋊S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C4 ◁ C8 | |
124 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^3,3,5,2^3|b^2=c,c^2=h,f^2=h,g^2=h,b^a=bh,d^a=d^2,e^a=e^4,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5405, #14512945, #14512952, … |
| maximal normal subgroup of | D5×#5405, #14512945, #14512952, … |
| maximal quotient of | #14511922, #14511924, #14511932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6319);