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C2×C11×D609 #40999697

order26796
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D609
unambiguous semidirect product(C2×C3)⋊(C11×D203)
unambiguous semidirect product(C2×C7)⋊(C11×D87)
unambiguous semidirect product(C2×C29)⋊(C11×D21)

Splittings

Fitting, socleC2×C3×C7×C11×C29 ⋊ C2
derived, HallC3×C7×C29 ⋊ C22×C11
HallC3×C7×C11×C29 ⋊ C22
HallC7×C11×C29 ⋊ C2×D3
HallC3×C11×C29 ⋊ C2×D7
HallC11×C29 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×D29
HallC7×C29 ⋊ C2×D3×C11
HallC3×C29 ⋊ C2×C11×D7
HallC7×C11 ⋊ C2×D87
HallC3×C11 ⋊ C2×D203
SylowC29 ⋊ C2×C11×D21
HallC3×C7 ⋊ C2×C11×D29
SylowC7 ⋊ C2×C11×D87
SylowC3 ⋊ C2×C11×D203

Subgroups

subgroupG/H
center, hypercenterC2×C11D609
commutator, cosocle, hypocenterC3×C7×C29C22×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C29C2
LCSG ▷ C3×C7×C29
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13398

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26796, 130);