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C7×(C5⋊D5)⋊D17 #26045451

order11900
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×(C5⋊D5)⋊D17
unambiguous semidirect product(C5⋊D5)⋊(C7×D17)
unambiguous semidirect productD85⋊(C7×D5)

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C22
derived, HallC52×C17 ⋊ C22×C7
HallC52×C7 ⋊ C2×D17
HallC7×C17 ⋊ D52
SylowC52 ⋊ C2×C7×D17
SylowC17 ⋊ C7×D52

Subgroups

subgroupG/H
center, hypercenterC7(C5⋊D5)⋊D17
commutator, cosocle, hypocenterC52×C17C22×C7
FrattiniC1G
Fitting, socleC52×C7×C17C22
LCSG ▷ C52×C17
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

896 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×((C5⋊D5)⋊C3)⋊D17, ΓL(1,𝔽8)×(C5⋊D5)⋊D17, C3×C7×(C5⋊D5)⋊D17, …
maximal normal subgroup ofΓL(1,𝔽8)×(C5⋊D5)⋊D17, C3×C7×(C5⋊D5)⋊D17
maximal quotient ofC3×C7×(C5⋊D5)⋊D17, C7×D85⋊D15, C7×#19099830

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 100);