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ΓL(1,𝔽8)×D737 #44526261

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

Aliases

direct productΓL(1,𝔽8)×D737
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×D67)

Splittings

Fitting, socle, derived, HallC7×C11×C67 ⋊ C2×C3
HallC11×ΓL(1,𝔽8)×C67 ⋊ C2
HallC7×D737 ⋊ C3
HallΓL(1,𝔽8)×C67 ⋊ D11
HallC11×C67 ⋊ C2×ΓL(1,𝔽8)
HallC7×C67 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ D67
HallC7×C11 ⋊ C3×D67
SylowC67 ⋊ ΓL(1,𝔽8)×D11
SylowC11 ⋊ ΓL(1,𝔽8)×D67
SylowC7 ⋊ C3×D737

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C67C2×C3
LCSG ▷ C7×C11×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 42);