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AGL(1,𝔽5)×#1004 #14479253

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#1004

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C4×H(5,𝔽2)
SylowC5 ⋊ C4×#1004
SylowC3 ⋊ AGL(1,𝔽5)×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC2×C3×C5×D4C2×C4
prime radicalD5×#1004C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×D4

3320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), AGL(1,𝔽5)×#5032, AGL(1,𝔽5)×#4741, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), AGL(1,𝔽5)×#5032, AGL(1,𝔽5)×#4741, …
maximal quotient of#72260127, #72260169, C3×AGL(1,𝔽5)×#1004, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204951);