Finite Group Databasebeta

C2×#29509842 #44527528

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

Aliases

direct productC2×#29509842

Splittings

derived, HallC7×C13×C19 ⋊ C2×C9
HallC2×C7×C13×C19 ⋊ C9
HallC2×C13×C19 ⋊ C7⋊C9
HallC2×C7×C19 ⋊ C13⋊C9
HallC13×C19 ⋊ C2×C7⋊C9
HallC2×C7×C13 ⋊ #4294
HallC7×C19 ⋊ C2×C13⋊C9
HallC7×C13 ⋊ C2×#4294
HallC2×C19 ⋊ #11717941
HallC2×C13 ⋊ #11924777
SylowC19 ⋊ C2×#11717941
HallC2×C7 ⋊ #14555736
SylowC13 ⋊ C2×#11924777
SylowC7 ⋊ C2×#14555736

Subgroups

subgroupG/H
center, hypercenterC2×C3#19104441
commutator, hypocenterC7×C13×C19C2×C9
FrattiniC3C2×#19104441
Fitting, socle, prime radicalC2×C3×C7×C13×C19C3
cosocleC3×C7×C13×C19C2×C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31122

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, 11);