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C17×D15⋊D7 #20297477

order7140
isoclinismisoclinic class of D15⋊D7
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×D15⋊D7
unambiguous semidirect productD15⋊(D7×C17)
unambiguous semidirect productD21⋊(D5×C17)
unambiguous semidirect productD35⋊(D3×C17)

Splittings

Fitting, socle, HallC3×C5×C7×C17 ⋊ C22
derived, HallC3×C5×C7 ⋊ C22×C17
HallC5×C7×C17 ⋊ C2×D3
HallC3×C7×C17 ⋊ C2×D5
HallC3×C5×C17 ⋊ C2×D7
HallC7×C17 ⋊ D3×D5
HallC5×C17 ⋊ D3×D7
HallC3×C17 ⋊ D5×D7
HallC5×C7 ⋊ C2×D3×C17
HallC3×C7 ⋊ C2×D5×C17
HallC3×C5 ⋊ C2×D7×C17
SylowC7 ⋊ D3×D5×C17
SylowC5 ⋊ D3×D7×C17
SylowC3 ⋊ D5×D7×C17

Subgroups

subgroupG/H
center, hypercenterC17D15⋊D7
commutator, hypocenterC3×C5×C7C22×C17
FrattiniC1G
Fitting, socleC3×C5×C7×C17C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

663 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×D35⋊D9, C17×D15⋊AGL(1,𝔽7), C3×C17×D15⋊D7, …
maximal normal subgroup ofC17×D15⋊AGL(1,𝔽7), C3×C17×D15⋊D7, C5×C17×D15⋊D7
maximal quotient ofC17×D35⋊D9, C3×C17×D15⋊D7, C17×D21⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7140, 107);