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C5×C23×#63271 #44536034

order31395
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×#63271

Splittings

Fitting, socle, HallC5×C7×C13×C23 ⋊ C3
derived, HallC7×C13 ⋊ C3×C5×C23
HallC7×C13×C23 ⋊ C3×C5
HallC5×C13×C23 ⋊ ΓL(1,𝔽8)
HallC5×C7×C23 ⋊ C13⋊C3
HallC5×C7×C13 ⋊ C3×C23
HallC13×C23 ⋊ C5×ΓL(1,𝔽8)
HallC7×C23 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ ΓL(1,𝔽8)×C23
HallC5×C7 ⋊ C23×C13⋊C3
SylowC13 ⋊ C5×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C5×C23×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C23#63271
commutator, cosocle, hypocenterC7×C13C3×C5×C23
FrattiniC1G
Fitting, socleC5×C7×C13×C23C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10465

Conjugacy classes & character table

3795 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31395, 5);