Finite Group Databasebeta

← Prev (#22604662) Next (#22604664) →

C17⋊#10587720 #22604663

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

Aliases

unambiguous semidirect productC17⋊#10587720

Splittings

Fitting, socle, derived, HallC7×C13×C17 ⋊ C2×C3
HallC17×#63270 ⋊ C2
HallC13×D119 ⋊ C3
Hall#63270 ⋊ D17
HallD119 ⋊ C13⋊C3
HallC13×C17 ⋊ AGL(1,𝔽7)
HallC7×C17 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C3×D17
SylowC17 ⋊ #10587720
SylowC13 ⋊ C17⋊AGL(1,𝔽7)
SylowC7 ⋊ D17×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C13×C17C2×C3
LCSG ▷ C7×C13×C17
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,13,17|c^a=c^6,e^a=e^16,c^b=c^2,d^b=d^3

Conjugacy classes & character table

291 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10587716⋊D17, #10587722⋊D17, D17×#10587720, …
maximal normal subgroup of#10587716⋊D17, #10587722⋊D17, D17×#10587720, …
maximal quotient of#32915444, C2×C17⋊#10587720, C17⋊#13109900, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 39);