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C2×ΓL(1,𝔽8)×D221 #32915554

order18564
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×ΓL(1,𝔽8)×D221
unambiguous semidirect product(C2×C17)⋊(ΓL(1,𝔽8)×D13)

Splittings

Fitting, socleC2×C7×C13×C17 ⋊ C2×C3
derived, HallC7×C13×C17 ⋊ C22×C3
HallC2×C7×D221 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×D17
HallC13×C17 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D17
SylowC17 ⋊ C2×ΓL(1,𝔽8)×D13
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D17
SylowC7 ⋊ C2×C3×D221

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D221
commutator, cosocle, hypocenterC7×C13×C17C22×C3
FrattiniC1G
Fitting, socleC2×C7×C13×C17C2×C3
LCSG ▷ C7×C13×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3094

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 149);