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C2×C3×#19104443 #44528021

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

Aliases

direct productC2×C3×#19104443

Splittings

Fitting, socleC2×C3×C7×C13×C19 ⋊ C3
derived, HallC7×C13×C19 ⋊ C2×C32
HallC2×C7×C13×C19 ⋊ C32
HallC2×C13×C19 ⋊ C3×ΓL(1,𝔽8)
HallC2×C7×C19 ⋊ C3×C13⋊C3
HallC13×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C7×C13 ⋊ C3×C19⋊C3
HallC7×C19 ⋊ C2×C3×C13⋊C3
HallC7×C13 ⋊ C2×C3×C19⋊C3
HallC2×C19 ⋊ C3×#63271
HallC2×C13 ⋊ C3×#87704
SylowC19 ⋊ C2×C3×#63271
HallC2×C7 ⋊ C3×#10625203
SylowC13 ⋊ C2×C3×#87704
SylowC7 ⋊ C2×C3×#10625203

Subgroups

subgroupG/H
center, hypercenterC2×C3#19104443
commutator, cosocle, hypocenterC7×C13×C19C2×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C19C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10374

Conjugacy classes & character table

3474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 504);