Finite Group Databasebeta

← Prev (#44568516) Next (#44568518) →

C11×C3⋊(C7⋊Dic35) #44568517

order32340
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×C3⋊(C7⋊Dic35)
unambiguous semidirect productC3⋊(C11×C7⋊Dic35)
unambiguous semidirect productC7⋊(C11×Dic105)

Splittings

derived, HallC3×C5×C72 ⋊ C4×C11
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ Dic5
HallC72×C11 ⋊ Dic15
HallC5×C72 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C11×Dic5
HallC5×C11 ⋊ C3⋊(C7⋊Dic7)
SylowC72 ⋊ C11×Dic15
HallC3×C11 ⋊ C7⋊Dic35
HallC3×C5 ⋊ C11×C7⋊Dic7
SylowC5 ⋊ C11×C3⋊(C7⋊Dic7)
SylowC3 ⋊ C11×C7⋊Dic35

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊(C7⋊D7))
commutator, hypocenterC3×C5×C72C4×C11
FrattiniC2C11×C3⋊(C5⋊(C7⋊D7))
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3×C5×C72C2×C11
LCSG ▷ C3×C5×C72
UCSC1 ◁ C2×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 219);