Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ (C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ #63579 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | ΓL(1,𝔽16)⋊D3 |
| commutator | C2×C32×C5 | C42 |
| Fitting, socle | C22×C32×C5 | C2×C4 |
| prime radical, cosocle | C22×C32×D5 | C22 |
| hypocenter | C32×C5 | #95 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
358 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 101 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:
2^5,3^2,5|a^2=c,b^2=d,b^a=be,f^a=f^2,h^a=h^2,f^b=f^2,g^b=g^2,h^c=h^484 conjugacy classes — view the full character table.
| maximal subgroup of | #72260236, AGL(1,𝔽5)×(C2×D3)⋊Dic3, #72260283 |
| maximal normal subgroup of | #72260236, AGL(1,𝔽5)×(C2×D3)⋊Dic3, #72260283 |
| maximal quotient of | #72230112, #72260235 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1804);