Finite Group Databasebeta

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#99×AGL(1,ℤ/25) #72275786

order16000
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct product#99×AGL(1,ℤ/25)

Splittings

Fitting#99×5−1+2 ⋊ C4
Sylow5−1+2 ⋊ C4×#99

Subgroups

subgroupG/H
centerC2C22⋊C4×AGL(1,ℤ/25)
commutatorC22×C25C2×C42×C5
FrattiniC23×C5C22×C5×AGL(1,𝔽5)
Fitting#99×5−1+2C4
socleC2×C5C5×C22⋊C4×AGL(1,𝔽5)
prime radicalC2×D4×D25⋊C5C22
cosocleC23×D25C23×C5
hypercenter#99AGL(1,ℤ/25)
hypocenterC25C4×C5×#99
LCSG ▷ C22×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C23 ◁ #99

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

286 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)

GAP

Past the SmallGroups library coverage — no SmallGroups id.