Finite Group Databasebeta

C2×#29509855 #44527801

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

Aliases

direct productC2×#29509855

Splittings

Fitting, socle, HallC2×C7×C13×C19 ⋊ C9
derived, HallC7×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C7⋊C9
HallC2×C7×C19 ⋊ C13⋊C9
HallC13×C19 ⋊ C2×C7⋊C9
HallC2×C7×C13 ⋊ #4296
HallC7×C19 ⋊ C2×C13⋊C9
HallC7×C13 ⋊ C2×#4296
HallC2×C19 ⋊ #11717941
HallC2×C13 ⋊ #11924781
SylowC19 ⋊ C2×#11717941
HallC2×C7 ⋊ #14555740
SylowC13 ⋊ C2×#11924781
SylowC7 ⋊ C2×#14555740

Subgroups

subgroupG/H
center, hypercenterC2#29509855
commutator, hypocenterC7×C13×C19C2×C9
FrattiniC1G
Fitting, socleC2×C7×C13×C19C9
prime radicalC2×C7×C13×C19⋊C3C3
cosocleC7×C13×C19⋊C3C2×C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 284);