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C7×C17⋊(D13⋊C3) #22604653

order9282
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17⋊(D13⋊C3)
unambiguous semidirect productC17⋊(C7×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C7×D17)
unambiguous semidirect productD221⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C3×C7
HallC7×C17×C13⋊C3 ⋊ C2
HallC7×D221 ⋊ C3
HallC17×C13⋊C3 ⋊ C2×C7
HallD221 ⋊ C3×C7
HallC7×C13⋊C3 ⋊ D17
HallC7×C17 ⋊ D13⋊C3
HallC7×C13 ⋊ C3×D17
HallC13⋊C3 ⋊ C7×D17
SylowC17 ⋊ C7×D13⋊C3
SylowC13 ⋊ C3×C7×D17

Subgroups

subgroupG/H
center, hypercenterC7C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C2×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C13×C17
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

448 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#11725130⋊C3, C7×#11725131⋊C3, C7×D17×D13⋊C3, …
maximal normal subgroup ofC7×#11725130⋊C3, C7×#11725131⋊C3, C7×D17×D13⋊C3, …
maximal quotient ofC7×Dic221⋊C3, C2×C7×C17⋊(D13⋊C3), C7×C17⋊(D13⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 29);