Finite Group Databasebeta

← Prev (#46801970) Next (#46801972) →

C22×C31×C11⋊C25 #46801971

order34100
automorphism?
homologyAbelianization (H1) = C22×C25×C31 · Schur multiplier (H2) = C2

Aliases

direct productC22×C31×C11⋊C25
unambiguous semidirect product(C22×C11)⋊(C25×C31)

Splittings

derived, SylowC11 ⋊ C22×C25×C31
HallC22×C11×C31 ⋊ C25
HallC11×C31 ⋊ C22×C25
HallC22×C11 ⋊ C25×C31

Subgroups

subgroupG/H
center, hypercenterC22×C5×C31C11⋊C5
commutator, hypocenterC11C22×C25×C31
FrattiniC5C22×C31×C11⋊C5
Fitting, socle, prime radicalC22×C5×C11×C31C5
cosocleC5×C11C22×C5×C31
LCSG ▷ C11
UCSC1 ◁ C22×C5×C31

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34100

Conjugacy classes & character table

4340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 62);