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C7×C5⋊(ΓL(1,𝔽8)⋊D23) #46798946

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(ΓL(1,𝔽8)⋊D23)
unambiguous semidirect productC5⋊(C7×ΓL(1,𝔽8)⋊D23)
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×D115)
unambiguous semidirect productC23⋊(C7×C5⋊AGL(1,𝔽7))
unambiguous semidirect productD805⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derivedC5×C7×C23 ⋊ C2×C3×C7
HallC5×C7×ΓL(1,𝔽8)×C23 ⋊ C2
HallC7×D805 ⋊ C3
HallC7×ΓL(1,𝔽8)×C23 ⋊ D5
HallC72×C23 ⋊ C3×D5
HallC5×C7×ΓL(1,𝔽8) ⋊ D23
HallC5×C72 ⋊ C3×D23
HallC7×ΓL(1,𝔽8) ⋊ D115
HallC5×C23 ⋊ C7×AGL(1,𝔽7)
SylowC72 ⋊ C3×D115
SylowC23 ⋊ C7×C5⋊AGL(1,𝔽7)
SylowC5 ⋊ C7×ΓL(1,𝔽8)⋊D23

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(ΓL(1,𝔽8)⋊D23)
commutator, cosocle, hypocenterC5×C7×C23C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C5×C7×C23
UCSC1 ◁ C7

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 50);