Finite Group Databasebeta

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ΓL(1,𝔽8)×D15×C31 #34086276

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D15×C31
unambiguous semidirect productC3⋊(D5×ΓL(1,𝔽8)×C31)
unambiguous semidirect productC5⋊(D3×ΓL(1,𝔽8)×C31)
unambiguous semidirect product(C7×D15)⋊(C3×C31)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derivedC3×C5×C7 ⋊ C2×C3×C31
HallC3×C5×ΓL(1,𝔽8)×C31 ⋊ C2
HallC3×ΓL(1,𝔽8)×C31 ⋊ D5
HallC5×C7×C31 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C31
HallC7×C31 ⋊ C3×D15
HallC5×C31 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D5×C31
HallC5×C7 ⋊ C3×D3×C31
SylowC7 ⋊ C3×D15×C31
SylowC5 ⋊ D3×ΓL(1,𝔽8)×C31

Subgroups

subgroupG/H
center, hypercenterC31ΓL(1,𝔽8)×D15
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C31
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

1395 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 181);