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C7×C17×D13⋊C3 #22604649

order9282
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×C17)
unambiguous semidirect product(C13⋊C3)⋊(C2×C7×C17)
unambiguous semidirect product(C17×D13)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C7×C17
HallC7×C17×C13⋊C3 ⋊ C2
HallC7×C17×D13 ⋊ C3
HallC17×C13⋊C3 ⋊ C2×C7
HallC17×D13 ⋊ C3×C7
HallC7×C13⋊C3 ⋊ C2×C17
HallC13×C17 ⋊ C2×C3×C7
HallC7×D13 ⋊ C3×C17
HallC7×C13 ⋊ C2×C3×C17
HallC13⋊C3 ⋊ C2×C7×C17
HallD13 ⋊ C3×C7×C17

Subgroups

subgroupG/H
center, hypercenterC7×C17D13⋊C3
commutator, hypocenterC13C2×C3×C7×C17
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C13
UCSC1 ◁ C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C17×AGL(1,𝔽13), C7×#11725132⋊C3, C7×D17×D13⋊C3, …
maximal normal subgroup ofC7×C17×AGL(1,𝔽13), C7×#11725132⋊C3, C7×D17×D13⋊C3, …
maximal quotient ofC7×C17×Dic13⋊C3, C2×C7×C17×D13⋊C3, C7×C17×D13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 25);