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C17×(C13⋊C3)⋊D7 #22604665

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

Aliases

direct productC17×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(D7×C17)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C17
HallC7×C17×C13⋊C3 ⋊ C2
HallC17×D91 ⋊ C3
HallC17×C13⋊C3 ⋊ D7
HallC7×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C3×D7
HallD91 ⋊ C3×C17
HallC7×C17 ⋊ D13⋊C3
HallC13⋊C3 ⋊ D7×C17
SylowC13 ⋊ C3×D7×C17
SylowC7 ⋊ C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17(C13⋊C3)⋊D7
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

493 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×(C13⋊C3)⋊D7, D7×C17×D13⋊C3, ((C13⋊C3)⋊D7)⋊D17, …
maximal normal subgroup ofD17×(C13⋊C3)⋊D7, D7×C17×D13⋊C3, ((C13⋊C3)⋊D7)⋊D17, …
maximal quotient ofC17×#11763955, C2×C17×(C13⋊C3)⋊D7, C17×(C13⋊C9)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 41);