Finite Group Databasebeta

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C2×C5×(C67⋊C3)⋊C11 #36348609

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×(C67⋊C3)⋊C11
unambiguous semidirect product(C2×C67⋊C3)⋊(C5×C11)
unambiguous semidirect product(C2×C67⋊C11)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C67⋊C3)⋊C11
unambiguous semidirect product(C2×C5×C67⋊C11)⋊C3

Splittings

Fitting, socle, HallC2×C5×C67 ⋊ C3×C11
derived, SylowC67 ⋊ C2×C3×C5×C11
HallC2×C5×C67⋊C11 ⋊ C3
HallC5×C67⋊C11 ⋊ C2×C3
HallC2×C5×C67⋊C3 ⋊ C11
HallC2×C67⋊C11 ⋊ C3×C5
HallC5×C67⋊C3 ⋊ C2×C11
HallC67⋊C11 ⋊ C2×C3×C5
HallC2×C67⋊C3 ⋊ C5×C11
HallC5×C67 ⋊ C2×C3×C11
HallC67⋊C3 ⋊ C2×C5×C11
HallC2×C67 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5(C67⋊C3)⋊C11
commutator, cosocle, hypocenterC67C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C67C3×C11
LCSG ▷ C67
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 670

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 5);