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C17×ΓL(1,𝔽8)×C29 #23780440

order10353
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C17×C29 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×C29
unambiguous semidirect productC7⋊(C3×C17×C29)
unambiguous semidirect product(C7×C17)⋊(C3×C29)
unambiguous semidirect product(C7×C29)⋊(C3×C17)
unambiguous semidirect product(C7×C17×C29)⋊C3

Splittings

Fitting, socle, HallC7×C17×C29 ⋊ C3
derived, SylowC7 ⋊ C3×C17×C29
HallC7×C29 ⋊ C3×C17
HallC7×C17 ⋊ C3×C29

Subgroups

subgroupG/H
center, hypercenterC17×C29ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C17×C29
FrattiniC1G
Fitting, socleC7×C17×C29C3
LCSG ▷ C7
UCSC1 ◁ C17×C29

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2465 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17×ΓL(1,𝔽8)×C29, C17×ΓL(1,𝔽8)×D29, ΓL(1,𝔽8)×C29×D17, …
maximal normal subgroup ofC2×C17×ΓL(1,𝔽8)×C29, C17×ΓL(1,𝔽8)×D29, ΓL(1,𝔽8)×C29×D17, …
maximal quotient ofC2×C17×ΓL(1,𝔽8)×C29, C17×C29×C7⋊C9, C3×C17×ΓL(1,𝔽8)×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10353, 3);