Finite Group Databasebeta

← Prev (#44528015) Next (#44528017) →

C2×C3×C13×#87705 #44528016

order31122
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C13×#87705

Splittings

Fitting, socleC2×C3×C7×C13×C19 ⋊ C3
derived, HallC7×C19 ⋊ C2×C32×C13
HallC2×C7×C13×C19 ⋊ C32
HallC7×C13×C19 ⋊ C2×C32
HallC2×C13×C19 ⋊ C3×ΓL(1,𝔽8)
HallC2×C7×C19 ⋊ C32×C13
HallC13×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C7×C13 ⋊ C3×C19⋊C3
HallC7×C13 ⋊ C2×C3×C19⋊C3
HallC2×C19 ⋊ C3×C13×ΓL(1,𝔽8)
SylowC19 ⋊ C2×C3×C13×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C13×C19⋊C3
SylowC7 ⋊ C2×C3×C13×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13#87705
commutator, cosocle, hypocenterC7×C19C2×C32×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C19C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10374

Conjugacy classes & character table

3666 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 499);