Finite Group Databasebeta

← Prev (#37524503) Next (#37524505) →

C2×C72×D13⋊C9 #37524504

order22932
automorphism?
homologyAbelianization (H1) = C22×C72×C9 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D13⋊C9
unambiguous semidirect productD13⋊(C2×C72×C9)
unambiguous semidirect product(C2×D13)⋊(C72×C9)
unambiguous semidirect product(C13⋊C9)⋊(C22×C72)
unambiguous semidirect product(C2×C13⋊C9)⋊(C2×C72)

Splittings

derived, SylowC13 ⋊ C22×C72×C9
HallC72×C13⋊C9 ⋊ C22
HallC2×C72×D13 ⋊ C9
HallC72×C13 ⋊ C22×C9
HallC13⋊C9 ⋊ C22×C72
HallC2×D13 ⋊ C72×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72D13⋊C3
commutator, hypocenterC13C22×C72×C9
FrattiniC3C2×C72×D13⋊C3
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C72×D13C3
cosocleC3×C13C22×C3×C72
LCSG ▷ C13
UCSC1 ◁ C2×C3×C72

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

2352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 449);