Finite Group Databasebeta

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C5×C13×ΓL(1,𝔽8)×C23 #44536032

order31395
automorphism?
homologyAbelianization (H1) = C3×C5×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×ΓL(1,𝔽8)×C23
unambiguous semidirect productC7⋊(C3×C5×C13×C23)
unambiguous semidirect product(C5×C7)⋊(C3×C13×C23)
unambiguous semidirect product(C7×C23)⋊(C3×C5×C13)
unambiguous semidirect product(C5×C7×C23)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C7×C13×C23 ⋊ C3
derived, SylowC7 ⋊ C3×C5×C13×C23
HallC7×C13×C23 ⋊ C3×C5
HallC5×C7×C23 ⋊ C3×C13
HallC5×C7×C13 ⋊ C3×C23
HallC7×C23 ⋊ C3×C5×C13
HallC7×C13 ⋊ C3×C5×C23
HallC5×C7 ⋊ C3×C13×C23

Subgroups

subgroupG/H
center, hypercenterC5×C13×C23ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C5×C13×C23
FrattiniC1G
Fitting, socleC5×C7×C13×C23C3
LCSG ▷ C7
UCSC1 ◁ C5×C13×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10465

Conjugacy classes & character table

7475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31395, 3);