Finite Group Databasebeta

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C2×C7×C13×#4296 #44527793

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C13×#4296

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13#4296
commutator, hypocenterC19C2×C7×C9×C13
FrattiniC1G
Fitting, socleC2×C7×C13×C19C9
prime radicalC2×C7×C13×C19⋊C3C3
cosocleC19⋊C3C2×C3×C7×C13
LCSG ▷ C19
UCSC1 ◁ C2×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

2002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 276);