Finite Group Databasebeta

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C2×C3×C17×(C5⋊D5)⋊C3 #29505916

order15300
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C17 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×C17×(C5⋊D5)⋊C3
unambiguous semidirect product(C2×C5⋊D5)⋊(C32×C17)
unambiguous semidirect product(C2×C3×C5⋊D5)⋊(C3×C17)
unambiguous semidirect product(C2×C17×C5⋊D5)⋊C32
unambiguous semidirect product(C2×C3×C17×C5⋊D5)⋊C3

Splittings

Fitting, socleC2×C3×C52×C17 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C32×C17
HallC3×C17×C52⋊C3 ⋊ C22
HallC2×C17×C5⋊D5 ⋊ C32
HallC52×C17 ⋊ C22×C32
HallC3×C52⋊C3 ⋊ C22×C17
HallC2×C5⋊D5 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C22×C32×C17
FrattiniC1G
Fitting, socleC2×C3×C52×C17C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C17

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1530

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 302);