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C2×C11×#13064104 #44526225

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×#13064104

Splittings

Fitting, socle, HallC2×C7×C11×C67 ⋊ C3
derived, HallC7×C67 ⋊ C2×C3×C11
HallC7×C11×C67 ⋊ C2×C3
HallC2×C11×C67 ⋊ ΓL(1,𝔽8)
HallC2×C7×C67 ⋊ C3×C11
HallC11×C67 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C11 ⋊ C67⋊C3
HallC2×C67 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C2×C67⋊C3
SylowC67 ⋊ C2×C11×ΓL(1,𝔽8)
HallC2×C7 ⋊ C11×C67⋊C3
SylowC7 ⋊ C2×C11×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#13064104
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C67C3
LCSG ▷ C7×C67
UCSC1 ◁ C2×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10318

Conjugacy classes & character table

3498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 6);