Finite Group Databasebeta

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ΓL(1,𝔽8)×D15×C41 #38788966

order25830
automorphism?
homologyAbelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D15×C41
unambiguous semidirect productC3⋊(D5×ΓL(1,𝔽8)×C41)
unambiguous semidirect productC5⋊(D3×ΓL(1,𝔽8)×C41)
unambiguous semidirect product(C7×D15)⋊(C3×C41)
unambiguous semidirect product(C7×D15×C41)⋊C3

Splittings

Fitting, socleC3×C5×C7×C41 ⋊ C2×C3
derivedC3×C5×C7 ⋊ C2×C3×C41
HallC3×C5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC3×ΓL(1,𝔽8)×C41 ⋊ D5
HallC5×C7×C41 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C41
HallC7×C41 ⋊ C3×D15
HallC5×C41 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D5×C41
HallC5×C7 ⋊ C3×D3×C41
SylowC7 ⋊ C3×D15×C41
SylowC5 ⋊ D3×ΓL(1,𝔽8)×C41

Subgroups

subgroupG/H
center, hypercenterC41ΓL(1,𝔽8)×D15
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C41
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C41

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4305

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 70);