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C13×ΓL(1,𝔽8)×D17 #22604646

order9282
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×D17
unambiguous semidirect productC17⋊(C2×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D17)⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C3×C13
HallC13×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×C13×D17 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×D17 ⋊ C3×C13
HallC13×C17 ⋊ C2×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D17
SylowC17 ⋊ C2×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×D17

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)×D17
commutator, hypocenterC7×C17C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×ΓL(1,𝔽8)⋊#595, C13×D17×AGL(1,𝔽7), ΓL(1,𝔽8)⋊#11725133, …
maximal normal subgroup ofC13×ΓL(1,𝔽8)⋊#595, C13×D17×AGL(1,𝔽7), ΓL(1,𝔽8)⋊#11725133, …
maximal quotient ofC13×ΓL(1,𝔽8)×Dic17, C2×C13×ΓL(1,𝔽8)×D17, C13×D17×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 22);