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C7×ΓL(1,𝔽8)⋊#1039 #28413151

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(C5⋊AGL(1,𝔽7))
commutator, hypocenterC52×C7C3×C4×C7
FrattiniC2C7×C5⋊(C5⋊AGL(1,𝔽7))
Fitting, socleC2×C52×C72C2×C3
prime radicalC2×C52×C7×ΓL(1,𝔽8)C2
cosocleC2×C52×C7C2×C3×C7
LCSG ▷ C52×C7
UCSC1 ◁ C2×C7

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

938 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 330);