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C4×C7×ΓL(1,𝔽8)×C25 #28412910

order14700
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×ΓL(1,𝔽8)×C25
unambiguous semidirect product(C4×C7)⋊(C3×C7×C25)
unambiguous semidirect product(C4×C7×C25)⋊(C3×C7)

Splittings

Fitting, HallC4×C72×C25 ⋊ C3
derivedC7 ⋊ C3×C4×C7×C25
HallC72×C25 ⋊ C3×C4
HallC4×C72 ⋊ C3×C25
SylowC72 ⋊ C3×C4×C25

Subgroups

subgroupG/H
center, hypercenterC4×C7×C25ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C7×C25
FrattiniC2×C5C2×C5×C7×ΓL(1,𝔽8)
FittingC4×C72×C25C3
socleC2×C5×C72C2×C3×C5
prime radicalC2×C5×C7×ΓL(1,𝔽8)C2×C5
cosocleC2×C5×C7C2×C3×C5×C7
LCSG ▷ C7
UCSC1 ◁ C4×C7×C25

90 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, 89);