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C7×ΓL(1,𝔽8)⋊#1044 #28413264

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

Aliases

direct productC7×ΓL(1,𝔽8)⋊#1044
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×#1044)
unambiguous semidirect product(C7⋊#1044)⋊(C3×C7)

Splittings

Fitting, socle, HallC52×C72 ⋊ C3×C4
derivedC52×C7 ⋊ C3×C4×C7
HallC7×C7⋊#1044 ⋊ C3
HallC52×C7×ΓL(1,𝔽8) ⋊ C4
HallC7×ΓL(1,𝔽8) ⋊ #1044
SylowC72 ⋊ C3×#1044
SylowC52 ⋊ C7×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC7ΓL(1,𝔽8)⋊#1044
commutator, hypocenterC52×C7C3×C4×C7
FrattiniC1G
Fitting, socleC52×C72C3×C4
prime radicalC7×ΓL(1,𝔽8)×C5⋊D5C2
cosocleC7×C5⋊D5C2×C3×C7
LCSG ▷ C52×C7
UCSC1 ◁ C7

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 443);