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C2×C17×C3⋊(C5⋊D5) #19099844

order5100
isoclinismisoclinic class of C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C17×C3⋊(C5⋊D5)
unambiguous semidirect product(C2×C3)⋊(C17×C5⋊D5)
unambiguous semidirect product(C2×C5)⋊(C17×D15)

Splittings

Fitting, socleC2×C3×C52×C17 ⋊ C2
derived, HallC3×C52 ⋊ C22×C17
HallC3×C52×C17 ⋊ C22
HallC52×C17 ⋊ C2×D3
HallC3×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D3×C17
SylowC3 ⋊ C2×C17×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C22×C17
FrattiniC1G
Fitting, socleC2×C3×C52×C17C2
LCSG ▷ C3×C52
UCSC1 ◁ C2×C17

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17×C5⋊D45, C2×C17×C3⋊((C5⋊D5)⋊C3), D3×C17×C3⋊(C5⋊D5), …
maximal normal subgroup ofC2×C17×C3⋊((C5⋊D5)⋊C3), C2×C3×C17×C3⋊(C5⋊D5), C2×C7×C17×C3⋊(C5⋊D5)
maximal quotient ofC2×C17×C5⋊D45, D3×C17×C3⋊(C5⋊D5), C2×C17×C3⋊(C3⋊(C5⋊D5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 147);