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C2×C7×#14555739 #44527794

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×#14555739

Splittings

Fitting, socle, HallC2×C7×C13×C19 ⋊ C9
derived, HallC13×C19 ⋊ C2×C7×C9
HallC7×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C7×C9
HallC2×C7×C19 ⋊ C13⋊C9
HallC2×C7×C13 ⋊ #4296
HallC7×C19 ⋊ C2×C13⋊C9
HallC7×C13 ⋊ C2×#4296
HallC2×C19 ⋊ C7×C13⋊C9
HallC2×C13 ⋊ C7×#4296
SylowC19 ⋊ C2×C7×C13⋊C9
SylowC13 ⋊ C2×C7×#4296

Subgroups

subgroupG/H
center, hypercenterC2×C7#14555739
commutator, hypocenterC13×C19C2×C7×C9
FrattiniC1G
Fitting, socleC2×C7×C13×C19C9
prime radicalC2×C7×C13×C19⋊C3C3
cosocleC13×C19⋊C3C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 277);