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C7×ΓL(1,𝔽8)×Dic25 #28412901

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×ΓL(1,𝔽8)×Dic25
unambiguous semidirect product(C7×Dic25)⋊(C3×C7)

Splittings

derivedC7×C25 ⋊ C3×C4×C7
HallC72×Dic25 ⋊ C3
HallC7×ΓL(1,𝔽8)×C25 ⋊ C4
HallC72×C25 ⋊ C3×C4
SylowC72 ⋊ C3×Dic25
SylowC25 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C7ΓL(1,𝔽8)×D25
commutator, hypocenterC7×C25C3×C4×C7
FrattiniC2×C5C7×D5×ΓL(1,𝔽8)
FittingC2×C72×C25C2×C3
socleC2×C5×C72C3×D5
prime radicalC2×C5×C7×ΓL(1,𝔽8)D5
cosocleC2×C7×C25C2×C3×C7
LCSG ▷ C7×C25
UCSC1 ◁ C2×C7

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 80);