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C17×(C5⋊D5)⋊D7 #26045456

order11900
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×(C5⋊D5)⋊D7
unambiguous semidirect product(C5⋊D5)⋊(D7×C17)
unambiguous semidirect productD35⋊(D5×C17)

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C22
derived, HallC52×C7 ⋊ C22×C17
HallC52×C17 ⋊ C2×D7
HallC7×C17 ⋊ D52
SylowC52 ⋊ C2×D7×C17
SylowC7 ⋊ D52×C17

Subgroups

subgroupG/H
center, hypercenterC17(C5⋊D5)⋊D7
commutator, cosocle, hypocenterC52×C7C22×C17
FrattiniC1G
Fitting, socleC52×C7×C17C22
LCSG ▷ C52×C7
UCSC1 ◁ C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×((C5⋊D5)⋊C3)⋊D7, C17×(C5⋊AGL(1,𝔽7))⋊D5, C3×C17×(C5⋊D5)⋊D7, …
maximal normal subgroup ofC17×(C5⋊AGL(1,𝔽7))⋊D5, C3×C17×(C5⋊D5)⋊D7
maximal quotient ofC3×C17×(C5⋊D5)⋊D7, C17×D35⋊D15, C17×#14523665

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 105);