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C7×AGL(1,𝔽5)×C61 #22555409

order8540
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C61 · Schur multiplier (H2) = C1

Aliases

direct productC7×AGL(1,𝔽5)×C61

Splittings

Fitting, socle, HallC5×C7×C61 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C61
HallC5×C61 ⋊ C4×C7
HallC5×C7 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC7×C61AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C61
FrattiniC1G
Fitting, socleC5×C7×C61C4
LCSG ▷ C5
UCSC1 ◁ C7×C61

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2135 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×AGL(1,𝔽5)×C61⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C61, AGL(1,𝔽5)×#13046196, …
maximal normal subgroup ofC7×AGL(1,𝔽5)×C61⋊C3, AGL(1,𝔽5)×ΓL(1,𝔽8)×C61, AGL(1,𝔽5)×#13046196, …
maximal quotient ofC3×C7×AGL(1,𝔽5)×C61, C7×ΓL(1,𝔽16)×C61

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8540, 24);