Finite Group Databasebeta

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C4×C11×C67⋊C11 #44569829

order32428
automorphism?
homologyAbelianization (H1) = C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC4×C11×C67⋊C11
unambiguous semidirect product(C4×C67)⋊C112
unambiguous semidirect product(C4×C11×C67)⋊C11

Splittings

FittingC4×C11×C67 ⋊ C11
derived, SylowC67 ⋊ C4×C112
HallC4×C67 ⋊ C112

Subgroups

subgroupG/H
center, hypercenterC4×C11C67⋊C11
commutator, hypocenterC67C4×C112
FrattiniC2C2×C11×C67⋊C11
FittingC4×C11×C67C11
socleC2×C11×C67C2×C11
prime radicalC2×C11×C67⋊C11C2
cosocleC2×C67C2×C112
LCSG ▷ C67
UCSC1 ◁ C4×C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2948

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32428, 18);