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C61×C7⋊AGL(1,𝔽5) #22555413

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

Aliases

direct productC61×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(AGL(1,𝔽5)×C61)

Splittings

Fitting, socle, HallC5×C7×C61 ⋊ C4
derived, HallC5×C7 ⋊ C4×C61
HallC7×C61 ⋊ AGL(1,𝔽5)
HallC5×C61 ⋊ Dic7
SylowC7 ⋊ AGL(1,𝔽5)×C61
SylowC5 ⋊ Dic7×C61

Subgroups

subgroupG/H
center, hypercenterC61C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C61
FrattiniC1G
Fitting, socleC5×C7×C61C4
LCSG ▷ C5×C7
UCSC1 ◁ C61

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1037 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC61×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #38785070, #38785071, …
maximal normal subgroup ofC61×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #38785070, #38785071, …
maximal quotient ofC3×C61×C7⋊AGL(1,𝔽5), C61×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8540, 28);