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C2×C7×C5⋊D85 #26045461

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

Aliases

direct productC2×C7×C5⋊D85
unambiguous semidirect product(C2×C5)⋊(C7×D85)
unambiguous semidirect product(C2×C17)⋊(C7×C5⋊D5)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2
derived, HallC52×C17 ⋊ C22×C7
HallC52×C7×C17 ⋊ C22
HallC52×C7 ⋊ C2×D17
HallC7×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C7×D17
SylowC17 ⋊ C2×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊D85
commutator, cosocle, hypocenterC52×C17C22×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2
LCSG ▷ C52×C17
UCSC1 ◁ C2×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2996 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C17⋊((C5⋊D5)⋊C3), C2×C17⋊((C5⋊D5)⋊ΓL(1,𝔽8)), C2×ΓL(1,𝔽8)×C5⋊D85, …
maximal normal subgroup ofC2×C7×C17⋊((C5⋊D5)⋊C3), C2×C17⋊((C5⋊D5)⋊ΓL(1,𝔽8)), C2×ΓL(1,𝔽8)×C5⋊D85, …
maximal quotient ofD3×C7×C5⋊D85, C2×C3×C7×C5⋊D85, C2×C7×C3⋊(C5⋊D85)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 110);