Finite Group Databasebeta

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#67×D5⋊AGL(1,𝔽5) #72259792

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

Aliases

direct product#67×D5⋊AGL(1,𝔽5)

Splittings

FittingC22×C3×C52 ⋊ C22×C4
HallC3×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C2×C4×#67
SylowC3 ⋊ D4×D5⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC2C2×D3×D5⋊AGL(1,𝔽5)
commutator, socleC2×C3×C52C23×C4
FittingC22×C3×C52C22×C4
prime radicalD52×#67C2
cosocleC2×C3×C5⋊D5C24
hypercenterC22D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C22

1892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D4×D5⋊AGL(1,𝔽5), #72260127, #72260169
maximal normal subgroup ofD3×D4×D5⋊AGL(1,𝔽5), #72260127, #72260169

GAP

Past the SmallGroups library coverage — no SmallGroups id.