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C11×ΓL(1,𝔽8)⋊D67 #44526269

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

Aliases

direct productC11×ΓL(1,𝔽8)⋊D67
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D67)

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, HallC7×C67 ⋊ C2×C3×C11
HallC11×ΓL(1,𝔽8)×C67 ⋊ C2
HallC11×D469 ⋊ C3
HallΓL(1,𝔽8)×C67 ⋊ C2×C11
HallD469 ⋊ C3×C11
HallC11×C67 ⋊ AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ D67
HallC7×C11 ⋊ C3×D67
SylowC67 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C11×D67
SylowC7 ⋊ C3×C11×D67

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊D67
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C67
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 50);