Finite Group Databasebeta

← Prev (#44526226) Next (#44526228) →

C2×ΓL(1,𝔽8)×C67⋊C11 #44526227

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×C67⋊C11
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C67C3×C11
LCSG ▷ C7×C67
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 938

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 8);