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D5×#3811 #13089041

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

Aliases

direct productD5×#3811

Splittings

FittingC22×C32×C5 ⋊ C23
HallC32×C5 ⋊ C22×D4
SylowC32 ⋊ C2×D4×D5
SylowC5 ⋊ C2×#3811

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×D5
commutator, socle, cosocleC2×C32×C5C24
FittingC22×C32×C5C23
hypercenterC22D32×D5
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 60

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3811, #72224623, C2×D5×#3811, …
maximal normal subgroup ofAGL(1,𝔽5)×#3811, C2×D5×#3811, D32×D4×D5, …
maximal quotient of#72224623, D5×#63930, D5×#63937, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5358);