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C17×#10587716 #22604651

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

Aliases

direct productC17×#10587716

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C17
HallC17×#63270 ⋊ C2
HallC7×C17×D13 ⋊ C3
HallC17×D13 ⋊ ΓL(1,𝔽8)
Hall#63270 ⋊ C2×C17
HallC13×C17 ⋊ C2×ΓL(1,𝔽8)
HallC7×D13 ⋊ C3×C17
HallC7×C17 ⋊ D13⋊C3
HallD13 ⋊ C17×ΓL(1,𝔽8)
SylowC13 ⋊ C2×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17#10587716
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

408 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×#11763985, #32915467, C17×#10587716⋊C2, …
maximal normal subgroup ofC17×#11763985, #32915467, C17×#10587716⋊C2, …
maximal quotient ofC17×#11763957, C2×C17×#10587716, C17×#13109896, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 27);