Finite Group Databasebeta

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D4×#10597182 #72259816

order4800
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#10597182

Splittings

FittingC3×C52×D4 ⋊ C2×C4
HallC3×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C4×D3×D4
SylowC3 ⋊ D4×D5⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC2C22×#10597182
commutator, socleC2×C3×C52C23×C4
FittingC3×C52×D4C2×C4
prime radicalD4×D15⋊D5C2
cosocleC2×C3×C5⋊D5C24
hypercenterD4#10597182
hypocenterC3×C52C2×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ D4

1892 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 ofD3×D4×D5⋊AGL(1,𝔽5), #72260237, #72260362
maximal normal subgroup ofD3×D4×D5⋊AGL(1,𝔽5), #72260237, #72260362

GAP

Past the SmallGroups library coverage — no SmallGroups id.