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ΓL(1,𝔽8)×D19×C47 #49175809

order37506
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D19×C47

Splittings

Fitting, socle, HallC7×C19×C47 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C47
HallC19×ΓL(1,𝔽8)×C47 ⋊ C2
HallC7×D19×C47 ⋊ C3
HallC19×C47 ⋊ C2×ΓL(1,𝔽8)
HallC19×ΓL(1,𝔽8) ⋊ C2×C47
HallC7×C47 ⋊ C3×D19
HallC7×D19 ⋊ C3×C47
SylowC19 ⋊ C2×ΓL(1,𝔽8)×C47
SylowC7 ⋊ C3×D19×C47

Subgroups

subgroupG/H
center, hypercenterC47ΓL(1,𝔽8)×D19
commutator, cosocle, hypocenterC7×C19C2×C3×C47
FrattiniC1G
Fitting, socleC7×C19×C47C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6251

Conjugacy classes & character table

2585 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37506, 26);