Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C32×C5 ⋊ C2×D8 |
| Sylow | C32 ⋊ C2×#686 |
| Sylow | C5 ⋊ #63926 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10624029 |
| commutator, Fitting, cosocle | C32×C4×C5 | C23 |
| Frattini, hypercenter | C4 | D32×D5 |
| socle | C2×C32×C5 | C2×D4 |
| hypocenter | C32×C5 | C2×D8 |
| LCS | G ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
358 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3^2,5|d^2=e,b^a=bd,c^a=cd,d^a=de,h^a=h^4,d^b=de,f^b=f^2,d^c=de,g^c=g^281 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63926, #72230428, #72230430 |
| maximal normal subgroup of | D5×#63926, #72230428, #72230430 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1990);