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C2×D5×#626 #13088992

order1440
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5×#626

Splittings

HallC32×C5 ⋊ C22×D4
SylowC32 ⋊ C2×D4×D5
SylowC5 ⋊ C22×#626

Subgroups

subgroupG/H
center, hypercenterC22D32×D5
commutator, cosocleC2×C32×C5C24
FrattiniC2C2×D32×D5
Fitting, socleC22×C32×C5C23
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D5×#3811, C2×AGL(1,𝔽5)×#626, C2×#13088417, …
maximal normal subgroup ofC2×D5×#3811, C2×AGL(1,𝔽5)×#626, C2×#13088417, …
maximal quotient ofD5×#63981, D5×#63825, C2×#72224600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5309);