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C52×C13×ΓL(1,𝔽8) #20291982

order6825
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C52×C13 · Schur multiplier (H2) = C5

Aliases

direct productC52×C13×ΓL(1,𝔽8)
unambiguous semidirect productC7⋊(C3×C52×C13)
unambiguous semidirect product(C5×C7)⋊(C3×C5×C13)

Splittings

Fitting, socle, HallC52×C7×C13 ⋊ C3
derived, SylowC7 ⋊ C3×C52×C13
HallC52×C7 ⋊ C3×C13
HallC7×C13 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC52×C13ΓL(1,𝔽8)
commutator, hypocenterC7C3×C52×C13
FrattiniC1G
Fitting, socleC52×C7×C13C3
LCSG ▷ C7
UCSC1 ◁ C52×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1625 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52×C13×AGL(1,𝔽7), C52×ΓL(1,𝔽8)⋊D13, C52×ΓL(1,𝔽8)×D13, …
maximal normal subgroup ofC52×C13×AGL(1,𝔽7), C52×ΓL(1,𝔽8)⋊D13, C52×ΓL(1,𝔽8)×D13, …
maximal quotient ofC2×C52×C13×ΓL(1,𝔽8), C52×C13×C7⋊C9, C3×C52×C13×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6825, 14);