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AGL(1,𝔽5)×C307 #20259591

order6140
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C307 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C307

Splittings

Fitting, socle, HallC5×C307 ⋊ C4
derived, SylowC5 ⋊ C4×C307

Subgroups

subgroupG/H
center, hypercenterC307AGL(1,𝔽5)
commutator, hypocenterC5C4×C307
FrattiniC1G
Fitting, socleC5×C307C4
LCSG ▷ C5
UCSC1 ◁ C307

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1535 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C307⋊C3, C3×AGL(1,𝔽5)×C307, ΓL(1,𝔽16)×C307, …
maximal normal subgroup ofAGL(1,𝔽5)×C307⋊C3, C3×AGL(1,𝔽5)×C307, C5×AGL(1,𝔽5)×C307
maximal quotient ofC3×AGL(1,𝔽5)×C307, ΓL(1,𝔽16)×C307, #1035×C307, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6140, 6);