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C5×#20263624 #44540267

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#20263624

Splittings

Fitting, socle, HallC5×C7×C151 ⋊ C2×C3
derived, HallC7×C151 ⋊ C2×C3×C5
HallC5×#15691749 ⋊ C2
HallC5×C7×D151 ⋊ C3
Hall#15691749 ⋊ C2×C5
HallC7×D151 ⋊ C3×C5
HallC5×D151 ⋊ ΓL(1,𝔽8)
HallC5×C151 ⋊ C2×ΓL(1,𝔽8)
HallD151 ⋊ C5×ΓL(1,𝔽8)
SylowC151 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D151⋊C3
SylowC7 ⋊ C5×D151⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#20263624
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C151C2×C3
LCSG ▷ C7×C151
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5285

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 36);