Finite Group Databasebeta

← Prev (#43270678) Next (#43270680) →

C2×C11⋊#13049955 #43270679

order28644
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊#13049955
unambiguous semidirect product(C2×C11)⋊#13049955

Splittings

Fitting, socleC2×C7×C11×C31 ⋊ C2×C3
derived, HallC7×C11×C31 ⋊ C22×C3
HallC2×C7×D341 ⋊ C3
HallC11×#10620253 ⋊ C22
HallC2×D341 ⋊ ΓL(1,𝔽8)
Hall#10620253 ⋊ C2×D11
HallC11×C31 ⋊ C22×ΓL(1,𝔽8)
HallC7×C31 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×#13049955
SylowC7 ⋊ C2×C11⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C11⋊#13049955
commutator, cosocle, hypocenterC7×C11×C31C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C31C2×C3
LCSG ▷ C7×C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4774

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28644, 98);