Finite Group Databasebeta

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C2×#13088407 #72230273

order2880
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13088407

Splittings

HallC32×C5 ⋊ C22×C4⋊C4
SylowC32 ⋊ C22×C4⋊AGL(1,𝔽5)
SylowC5 ⋊ C2×#63883

Subgroups

subgroupG/H
center, hypercenterC22D32×AGL(1,𝔽5)
commutatorC2×C32×C5C23×C4
FrattiniC2C2×D32×AGL(1,𝔽5)
Fitting, socleC22×C32×C5C22×C4
prime radicalC22×D5×C3⋊D3C22
cosocleC2×C32×D5C24
hypocenterC32×C5C22×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

1908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#3811, C2×#72231400, #72260225
maximal normal subgroup ofC2×AGL(1,𝔽5)×#3811, #72260225
maximal quotient of#72230439, C2×#72231400

GAP

Past the SmallGroups library coverage — no SmallGroups id.