Finite Group Databasebeta

C2×C7×#14555736 #44527522

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

Aliases

direct productC2×C7×#14555736

Splittings

derived, HallC13×C19 ⋊ C2×C7×C9
HallC2×C7×C13×C19 ⋊ C9
HallC7×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C7×C9
HallC2×C7×C19 ⋊ C13⋊C9
HallC2×C7×C13 ⋊ #4294
HallC7×C19 ⋊ C2×C13⋊C9
HallC7×C13 ⋊ C2×#4294
HallC2×C19 ⋊ C7×C13⋊C9
HallC2×C13 ⋊ C7×#4294
SylowC19 ⋊ C2×C7×C13⋊C9
SylowC13 ⋊ C2×C7×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7#10625203
commutator, hypocenterC13×C19C2×C7×C9
FrattiniC3C2×C7×#10625203
Fitting, socle, prime radicalC2×C3×C7×C13×C19C3
cosocleC3×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31122

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 5);