Finite Group Databasebeta

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C2×C11×D67⋊C11 #44569837

order32428
automorphism?
homologyAbelianization (H1) = C22×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C11×D67⋊C11
unambiguous semidirect productD67⋊(C2×C112)
unambiguous semidirect product(C2×D67)⋊C112
unambiguous semidirect product(C67⋊C11)⋊(C22×C11)
unambiguous semidirect product(C2×C67⋊C11)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D67)⋊C11

Splittings

Fitting, socleC2×C11×C67 ⋊ C2×C11
derived, SylowC67 ⋊ C22×C112
HallC11×C67⋊C11 ⋊ C22
HallC2×D67 ⋊ C112

Subgroups

subgroupG/H
center, hypercenterC2×C11D67⋊C11
commutator, cosocle, hypocenterC67C22×C112
FrattiniC1G
Fitting, socleC2×C11×C67C2×C11
LCSG ▷ C67
UCSC1 ◁ C2×C11

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1474

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32428, 26);