Finite Group Databasebeta

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#120×AGL(1,ℤ/25) #72275659

order16000
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct product#120×AGL(1,ℤ/25)

Splittings

Fitting#120×5−1+2 ⋊ C4
Sylow5−1+2 ⋊ C4×#120

Subgroups

subgroupG/H
centerC22C23×AGL(1,ℤ/25)
commutatorC22×C25C23×C4×C5
Frattini, socleC22×C5C23×C5×AGL(1,𝔽5)
Fitting#120×5−1+2C4
prime radical#120×D25⋊C5C2
cosocleC22×D25C24×C5
hypercenter#120AGL(1,ℤ/25)
hypocenterC25C4×C5×#120
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #120

3737 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofB(4,𝔽2)×AGL(1,ℤ/25)
maximal normal subgroup ofB(4,𝔽2)×AGL(1,ℤ/25)
maximal quotient ofB(4,𝔽2)×AGL(1,ℤ/25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.