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AGL(1,𝔽25) #10597168

order600
isoclinismisoclinic class of AGL(1,𝔽25)
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽25)
unambiguous semidirect product#6053⋊C3

Splittings

Fitting, socle, derived, SylowC52 ⋊ C3×C8
Hall#6053 ⋊ C3
HallC52⋊C3 ⋊ C8

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52C3×C8
prime radical(C5⋊D5)⋊C3C4
cosocle#1043C2×C3
LCSG ▷ C52
UCSC1

19 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25

Polycyclic presentation:

2,3,2^2,5^2|a^2=c,c^2=d,e^a=e^2f^4,f^a=e^2f^3,e^b=e^3f^2,f^b=ef,e^c=e^2,f^c=f^2,e^d=e^4,f^d=f^4

Conjugacy classes & character table

25 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAΓL(1,𝔽25), C2×AGL(1,𝔽25), C3×AGL(1,𝔽25), …
maximal normal subgroup ofAΓL(1,𝔽25), C2×AGL(1,𝔽25), C3×AGL(1,𝔽25)
maximal quotient of#87822⋊C3, C2×AGL(1,𝔽25), #6053⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 149);