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C4×C52×C7×ΓL(1,𝔽8) #28413188

order14700
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52×C7×ΓL(1,𝔽8)
unambiguous semidirect product(C4×C7)⋊(C3×C52×C7)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C5×C7)

Splittings

Fitting, HallC4×C52×C72 ⋊ C3
derivedC7 ⋊ C3×C4×C52×C7
HallC52×C72 ⋊ C3×C4
HallC4×C72 ⋊ C3×C52
SylowC72 ⋊ C3×C4×C52

Subgroups

subgroupG/H
center, hypercenterC4×C52×C7ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C52×C7
FrattiniC2C2×C52×C7×ΓL(1,𝔽8)
FittingC4×C52×C72C3
socleC2×C52×C72C2×C3
prime radicalC2×C52×C7×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C52×C7
LCSG ▷ C7
UCSC1 ◁ C4×C52×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 367);