Finite Group Databasebeta

← Prev (#44526222) Next (#44526224) →

C2×C11×ΓL(1,𝔽8)×C67 #44526223

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C67 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×ΓL(1,𝔽8)×C67
unambiguous semidirect product(C2×C7)⋊(C3×C11×C67)
unambiguous semidirect product(C2×C7×C11)⋊(C3×C67)

Splittings

Fitting, socle, HallC2×C7×C11×C67 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C11×C67
HallC7×C11×C67 ⋊ C2×C3
HallC2×C7×C67 ⋊ C3×C11
HallC7×C67 ⋊ C2×C3×C11
HallC2×C7×C11 ⋊ C3×C67
HallC7×C11 ⋊ C2×C3×C67
HallC2×C7 ⋊ C3×C11×C67

Subgroups

subgroupG/H
center, hypercenterC2×C11×C67ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C11×C67
FrattiniC1G
Fitting, socleC2×C7×C11×C67C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10318

Conjugacy classes & character table

7370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 4);