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C7×C25×ΓL(1,𝔽8)⋊C4 #28412893

order14700
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C7×C25)
unambiguous semidirect productDic7⋊(C3×C7×C25)
unambiguous semidirect product(C25×Dic7)⋊(C3×C7)

Splittings

derivedC7 ⋊ C3×C4×C7×C25
HallC7×C25×Dic7 ⋊ C3
HallC7×ΓL(1,𝔽8)×C25 ⋊ C4
HallC72×C25 ⋊ C3×C4
HallC7×Dic7 ⋊ C3×C25
HallC7×ΓL(1,𝔽8) ⋊ C4×C25
SylowC72 ⋊ C3×C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C7×C25
FrattiniC2×C5C5×C7×AGL(1,𝔽7)
FittingC2×C72×C25C2×C3
socleC2×C5×C72C2×C3×C5
prime radicalC2×C5×C7×ΓL(1,𝔽8)C2×C5
cosocleC2×C5×C7C2×C3×C5×C7
LCSG ▷ C7
UCSC1 ◁ C2×C7×C25

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 72);