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ΓL(1,𝔽8)×D11×C67 #44526257

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C67 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D11×C67
unambiguous semidirect productC11⋊(C2×ΓL(1,𝔽8)×C67)
unambiguous semidirect product(C7×D11)⋊(C3×C67)

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C67
HallC11×ΓL(1,𝔽8)×C67 ⋊ C2
HallC7×D11×C67 ⋊ C3
HallC11×C67 ⋊ C2×ΓL(1,𝔽8)
HallC7×C67 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C67
HallC7×D11 ⋊ C3×C67
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C67
SylowC7 ⋊ C3×D11×C67

Subgroups

subgroupG/H
center, hypercenterC67ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C67
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

2345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 38);