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C17×ΓL(1,𝔽8)⋊D13 #22604666

order9282
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊D13
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D13)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C17
HallC13×C17×ΓL(1,𝔽8) ⋊ C2
HallC17×D91 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C17
HallC13×C17 ⋊ AGL(1,𝔽7)
HallD91 ⋊ C3×C17
HallC7×C17 ⋊ C3×D13
HallΓL(1,𝔽8) ⋊ C17×D13
SylowC13 ⋊ C17×AGL(1,𝔽7)
SylowC7 ⋊ C3×C17×D13

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C2×C3×C17
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×D13×AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D17, D17×ΓL(1,𝔽8)⋊D13, …
maximal normal subgroup ofC17×D13×AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D17, D17×ΓL(1,𝔽8)⋊D13, …
maximal quotient ofC17×ΓL(1,𝔽8)⋊Dic13, C2×C17×ΓL(1,𝔽8)⋊D13, C17×(C7⋊C9)⋊D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 42);