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C2×C11×D525 #37528326

order23100
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D525
unambiguous semidirect product(C2×C3)⋊(C11×D175)
unambiguous semidirect product(C2×C7)⋊(C11×D75)
unambiguous semidirect product(C2×C25)⋊(C11×D21)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC3×C7×C25 ⋊ C22×C11
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC11×C25 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D75
HallC3×C25 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×D175
SylowC25 ⋊ C2×C11×D21
HallC3×C7 ⋊ C2×C11×D25
SylowC7 ⋊ C2×C11×D75
SylowC3 ⋊ C2×C11×D175

Subgroups

subgroupG/H
center, hypercenterC2×C11D525
commutator, cosocle, hypocenterC3×C7×C25C22×C11
FrattiniC5C2×C11×D105
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11D5
LCSG ▷ C3×C7×C25
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 137);