Finite Group Databasebeta

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C2×C11×#13095531 #46803237

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×#13095531

Splittings

Fitting, socleC2×C7×C11×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C22×C3×C11
HallC2×C7×C11×D37 ⋊ C3
HallC11×#11715913 ⋊ C22
HallC7×C11×C37 ⋊ C22×C3
HallC2×C11×D37 ⋊ ΓL(1,𝔽8)
HallC2×C7×D37 ⋊ C3×C11
Hall#11715913 ⋊ C22×C11
HallC11×C37 ⋊ C22×ΓL(1,𝔽8)
HallC2×D37 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C2×D37⋊C3
SylowC37 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C11×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#13095531
commutator, cosocle, hypocenterC7×C37C22×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 109);