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C5×ΓL(1,𝔽8)×D161 #46798930

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D161
unambiguous semidirect productC23⋊(C5×D7×ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derived, HallC72×C23 ⋊ C2×C3×C5
HallC5×C7×ΓL(1,𝔽8)×C23 ⋊ C2
HallC5×C7×D161 ⋊ C3
HallC7×ΓL(1,𝔽8)×C23 ⋊ C2×C5
HallC7×D161 ⋊ C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ D23
HallC5×C72 ⋊ C3×D23
HallC7×ΓL(1,𝔽8) ⋊ C5×D23
HallC5×C23 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C5×D23
SylowC23 ⋊ C5×D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D161
commutator, cosocle, hypocenterC72×C23C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C72×C23
UCSC1 ◁ C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

2050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 34);