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AGL(1,𝔽5)×C277 #19149792

order5540
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C277 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C277

Splittings

Fitting, socle, HallC5×C277 ⋊ C4
derived, SylowC5 ⋊ C4×C277

Subgroups

subgroupG/H
center, hypercenterC277AGL(1,𝔽5)
commutator, hypocenterC5C4×C277
FrattiniC1G
Fitting, socleC5×C277C4
LCSG ▷ C5
UCSC1 ◁ C277

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1385 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C277⋊C3, C3×AGL(1,𝔽5)×C277, ΓL(1,𝔽16)×C277, …
maximal normal subgroup ofAGL(1,𝔽5)×C277⋊C3, C3×AGL(1,𝔽5)×C277, C5×AGL(1,𝔽5)×C277
maximal quotient ofC3×AGL(1,𝔽5)×C277, ΓL(1,𝔽16)×C277, #1035×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5540, 7);