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C17×#10587723 #22604668

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

Aliases

direct productC17×#10587723

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C17
HallC17×#63271 ⋊ C2
HallC17×D91 ⋊ C3
Hall#63271 ⋊ C2×C17
HallC13×C17 ⋊ AGL(1,𝔽7)
HallD91 ⋊ C3×C17
HallC7×C17 ⋊ D13⋊C3
SylowC13 ⋊ C17×AGL(1,𝔽7)
SylowC7 ⋊ C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17#10587723
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

357 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×#10587723, C17×#10587717⋊C2, #10587723⋊D17, …
maximal normal subgroup ofD17×#10587723, C17×#10587717⋊C2, #10587723⋊D17, …
maximal quotient ofC17×#11763964, C2×C17×#10587723, C17×#13109903, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 44);