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C2×C11×#10620252 #28384902

order14322
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×#10620252

Splittings

Fitting, socle, HallC2×C7×C11×C31 ⋊ C3
derived, HallC7×C31 ⋊ C2×C3×C11
HallC7×C11×C31 ⋊ C2×C3
HallC2×C11×C31 ⋊ ΓL(1,𝔽8)
HallC2×C7×C31 ⋊ C3×C11
HallC11×C31 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C11 ⋊ C31⋊C3
HallC7×C11 ⋊ C2×C31⋊C3
HallC2×C31 ⋊ C11×ΓL(1,𝔽8)
SylowC31 ⋊ C2×C11×ΓL(1,𝔽8)
HallC2×C7 ⋊ C11×C31⋊C3
SylowC7 ⋊ C2×C11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#10620252
commutator, cosocle, hypocenterC7×C31C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C31C3
LCSG ▷ C7×C31
UCSC1 ◁ C2×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4774

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×#10620252, C11×#14579595, Dic11×#10620252, …
maximal normal subgroup ofC4×C11×#10620252, C11×#14579595, Dic11×#10620252, …
maximal quotient ofC4×C11×#10620252, C22×C11×#10620252

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14322, 5);