Finite Group Databasebeta

← Prev (#37524828) Next (#37524830) →

C3×C3⋊(C7⋊Dic91) #37524829

order22932
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC3×C3⋊(C7⋊Dic91)
unambiguous semidirect productC3⋊(C3×C7⋊Dic91)

Splittings

derivedC3×C72×C13 ⋊ C3×C4
HallC32×C72×C13 ⋊ C4
HallC72×C13 ⋊ C3×Dic3
HallC32×C72 ⋊ Dic13
HallC32×C13 ⋊ C7⋊Dic7
SylowC72 ⋊ C3×Dic39
SylowC13 ⋊ C3×C3⋊(C7⋊Dic7)
SylowC32 ⋊ C7⋊Dic91

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C7⋊D91)
commutator, hypocenterC3×C72×C13C3×C4
FrattiniC2C3×C3⋊(C7⋊D91)
Fitting, socle, prime radicalC2×C32×C72×C13C2
cosocleC2×C3×C72×C13C2×C3
LCSG ▷ C3×C72×C13
UCSC1 ◁ C2×C3

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 774);