Finite Group Databasebeta

C2×C13×#11924776 #44527524

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

Aliases

direct productC2×C13×#11924776

Splittings

derived, HallC7×C19 ⋊ C2×C9×C13
HallC2×C7×C13×C19 ⋊ C9
HallC7×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C7⋊C9
HallC2×C7×C19 ⋊ C9×C13
HallC13×C19 ⋊ C2×C7⋊C9
HallC2×C7×C13 ⋊ #4294
HallC7×C13 ⋊ C2×#4294
HallC2×C19 ⋊ C13×C7⋊C9
SylowC19 ⋊ C2×C13×C7⋊C9
HallC2×C7 ⋊ C13×#4294
SylowC7 ⋊ C2×C13×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13#87704
commutator, hypocenterC7×C19C2×C9×C13
FrattiniC3C2×C13×#87704
Fitting, socle, prime radicalC2×C3×C7×C13×C19C3
cosocleC3×C7×C19C2×C3×C13
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31122

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, 7);