Finite Group Databasebeta

← Prev (#44568931) Next (#44568933) →

C2×C3×C5×C72×D11 #44568932

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C5×C72×D11

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derived, SylowC11 ⋊ C22×C3×C5×C72
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C22×C5
HallC72×C11 ⋊ C22×C3×C5
HallC3×C5×C11 ⋊ C22×C72
HallC5×C11 ⋊ C22×C3×C72
HallC3×C11 ⋊ C22×C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C72D11
commutator, cosocle, hypocenterC11C22×C3×C5×C72
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C72

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

10290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 634);