Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C5×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C5 ⋊ #5394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C2×C4 |
| Fitting | C5×Q8 | C4×D3 |
| socle | C2×C5 | C4×S4 |
| prime radical | D5×GL(2,𝔽3) | C2 |
| cosocle | D5×SL(2,𝔽3) | C22 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
154 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^3,3,5,2^3|a^2=c,f^2=h,g^2=h,b^a=bh,e^a=e^2,d^b=d^2,f^b=gh,g^b=fh,e^c=e^4,f^d=g,g^d=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11756705, AGL(1,𝔽5)×#983, #14514305, … |
| maximal normal subgroup of | C2×#11756705, AGL(1,𝔽5)×#983, #14514305, … |
| maximal quotient of | GL(2,𝔽3)⋊#170, #14512386, #14512387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10900);