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C7×D17×C5⋊D5 #26045442

order11900
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C22
derived, HallC52×C17 ⋊ C22×C7
HallC52×C7 ⋊ C2×D17
HallC7×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C7×D17
SylowC17 ⋊ C2×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC7D17×C5⋊D5
commutator, cosocle, hypocenterC52×C17C22×C7
FrattiniC1G
Fitting, socleC52×C7×C17C22
LCSG ▷ C52×C17
UCSC1 ◁ C7

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D17×(C5⋊D5)⋊C3, D17×(C5⋊D5)⋊ΓL(1,𝔽8), ΓL(1,𝔽8)×D17×C5⋊D5, …
maximal normal subgroup ofC7×D17×(C5⋊D5)⋊C3, D17×(C5⋊D5)⋊ΓL(1,𝔽8), ΓL(1,𝔽8)×D17×C5⋊D5, …
maximal quotient ofC3×C7×D17×C5⋊D5, C7×D17×C3⋊(C5⋊D5), C7×C5⋊D5×D51, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 91);