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C4×AGL(1,𝔽25) #72223554

order2400
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productC4×AGL(1,𝔽25)

Splittings

FittingC4×C52 ⋊ C3×C8
derived, SylowC52 ⋊ C3×C4×C8
HallC4×#6053 ⋊ C3
HallC52⋊C3 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽25)
commutator, hypocenterC52C3×C4×C8
FrattiniC2C2×AGL(1,𝔽25)
FittingC4×C52C3×C8
socleC2×C52C2×C3×C8
prime radicalC2×(C5⋊D5)⋊C3C2×C4
cosocleC2×#1043C22×C3
LCSG ▷ C52
UCSC1 ◁ C4

103 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×AGL(1,𝔽25), C8×AGL(1,𝔽25), C4×AΓL(1,𝔽25)
maximal normal subgroup ofC3×C4×AGL(1,𝔽25), C8×AGL(1,𝔽25), C4×AΓL(1,𝔽25)
maximal quotient ofC3×C4×AGL(1,𝔽25), C8×AGL(1,𝔽25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.