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C4×C11×#92789 #36373274

order22308
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C13

Aliases

direct productC4×C11×#92789

Splittings

Fitting, HallC4×C11×C132 ⋊ C3
derived, SylowC132 ⋊ C3×C4×C11
HallC11×C132 ⋊ C3×C4
HallC4×C132 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC4×C11#92789
commutator, hypocenterC132C3×C4×C11
FrattiniC2C2×C11×#92789
FittingC4×C11×C132C3
socleC2×C11×C132C2×C3
prime radicalC2×C11×#92789C2
cosocleC2×C132C2×C3×C11
LCSG ▷ C132
UCSC1 ◁ C4×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1716

Conjugacy classes & character table

2596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22308, 61);