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ΓL(1,𝔽8)×C23×D35 #46798949

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C23×D35
unambiguous semidirect productC5⋊(D7×ΓL(1,𝔽8)×C23)

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C23
HallC5×C7×ΓL(1,𝔽8)×C23 ⋊ C2
HallC7×C23×D35 ⋊ C3
HallC7×ΓL(1,𝔽8)×C23 ⋊ D5
HallC72×C23 ⋊ C3×D5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C23
HallC7×D35 ⋊ C3×C23
HallC7×ΓL(1,𝔽8) ⋊ D5×C23
HallC5×C23 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×D5×C23
SylowC5 ⋊ D7×ΓL(1,𝔽8)×C23

Subgroups

subgroupG/H
center, hypercenterC23ΓL(1,𝔽8)×D35
commutator, cosocle, hypocenterC5×C72C2×C3×C23
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C23

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

2185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 53);