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C2×C17⋊((C5⋊D5)⋊C3) #19099771

order5100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C17⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C17)⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C5⋊D85)⋊C3

Splittings

Fitting, socleC2×C52×C17 ⋊ C2×C3
derived, HallC52×C17 ⋊ C22×C3
HallC2×C5⋊D85 ⋊ C3
HallC17×C52⋊C3 ⋊ C22
HallC52⋊C3 ⋊ C2×D17
SylowC52 ⋊ C2×C3×D17
SylowC17 ⋊ C2×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C17⋊((C5⋊D5)⋊C3)
commutator, hypocenterC52×C17C22×C3
FrattiniC1G
Fitting, socleC2×C52×C17C2×C3
LCSG ▷ C52×C17
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C17⋊((C5⋊D5)⋊C3), C2×C3×C17⋊((C5⋊D5)⋊C3), C2×C3⋊(C17⋊((C5⋊D5)⋊C3)), …
maximal normal subgroup ofC2×C3×C17⋊((C5⋊D5)⋊C3), C2×C7×C17⋊((C5⋊D5)⋊C3)
maximal quotient ofC2×C17⋊((C5⋊D5)⋊C9), D3×C17⋊((C5⋊D5)⋊C3), C2×C3×C17⋊((C5⋊D5)⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 74);