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C3×D17×C5⋊D5 #19099792

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

Aliases

direct productC3×D17×C5⋊D5
unambiguous semidirect product(C5×D17)⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C52×C17 ⋊ C22
derived, HallC52×C17 ⋊ C22×C3
HallC3×C52 ⋊ C2×D17
HallC3×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C3×D17
SylowC17 ⋊ C2×C3×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3D17×C5⋊D5
commutator, hypocenterC52×C17C22×C3
FrattiniC1G
Fitting, socleC3×C52×C17C22
LCSG ▷ C52×C17
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×(C5⋊D5)⋊C9, C9×D17×C5⋊D5, C3×D17×(C5⋊D5)⋊C3, …
maximal normal subgroup ofD17×(C5⋊D5)⋊C9, C9×D17×C5⋊D5, C3×D17×(C5⋊D5)⋊C3, …
maximal quotient ofC9×D17×C5⋊D5, C32×D17×C5⋊D5, C3×D17×C3⋊(C5⋊D5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 95);