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C7×#1039⋊ΓL(1,𝔽8) #28413168

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×#1039⋊ΓL(1,𝔽8)
unambiguous semidirect product#1039⋊(C7×ΓL(1,𝔽8))

Splittings

derivedC52×C7 ⋊ C3×C4×C7
HallC72×#1039 ⋊ C3
HallC7×C7⋊(C52⋊C3) ⋊ C4
HallC52×C72 ⋊ C3×C4
Hall#1039 ⋊ C7×ΓL(1,𝔽8)
SylowC72 ⋊ #1039⋊C3
SylowC52 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C7(C5⋊D5)⋊ΓL(1,𝔽8)
commutator, hypocenterC52×C7C3×C4×C7
FrattiniC2C7×(C5⋊D5)⋊ΓL(1,𝔽8)
Fitting, socleC2×C52×C72C2×C3
prime radicalC2×C7×C7⋊(C52⋊C3)C2
cosocleC2×C52×C7C2×C3×C7
LCSG ▷ C52×C7
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 347);