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ΓL(1,𝔽8)×D13×C43 #37553470

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D13×C43

Splittings

Fitting, socle, HallC7×C13×C43 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C43
HallC13×ΓL(1,𝔽8)×C43 ⋊ C2
HallC7×D13×C43 ⋊ C3
HallC13×C43 ⋊ C2×ΓL(1,𝔽8)
HallC7×C43 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C43
HallC7×D13 ⋊ C3×C43
SylowC13 ⋊ C2×ΓL(1,𝔽8)×C43
SylowC7 ⋊ C3×D13×C43

Subgroups

subgroupG/H
center, hypercenterC43ΓL(1,𝔽8)×D13
commutator, cosocle, hypocenterC7×C13C2×C3×C43
FrattiniC1G
Fitting, socleC7×C13×C43C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3913

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 59);