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ΓL(1,𝔽8)×D15×C47 #44444102

order29610
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D15×C47
unambiguous semidirect productC3⋊(D5×ΓL(1,𝔽8)×C47)
unambiguous semidirect productC5⋊(D3×ΓL(1,𝔽8)×C47)
unambiguous semidirect product(C7×D15)⋊(C3×C47)
unambiguous semidirect product(C7×D15×C47)⋊C3

Splittings

Fitting, socleC3×C5×C7×C47 ⋊ C2×C3
derivedC3×C5×C7 ⋊ C2×C3×C47
HallC3×C5×ΓL(1,𝔽8)×C47 ⋊ C2
HallC3×ΓL(1,𝔽8)×C47 ⋊ D5
HallC5×C7×C47 ⋊ C3×D3
HallC7×C47 ⋊ C3×D15
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C47
HallC5×C47 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D5×C47
HallC5×C7 ⋊ C3×D3×C47
SylowC7 ⋊ C3×D15×C47
SylowC5 ⋊ D3×ΓL(1,𝔽8)×C47

Subgroups

subgroupG/H
center, hypercenterC47ΓL(1,𝔽8)×D15
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C47
FrattiniC1G
Fitting, socleC3×C5×C7×C47C2×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C47

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4935

Conjugacy classes & character table

2115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 39);