Finite Group Databasebeta

D11×C25×C59 #44570081

order32450
automorphism?
homologyAbelianization (H1) = C2×C25×C59 · Schur multiplier (H2) = C1

Aliases

direct productD11×C25×C59

Splittings

Fitting, HallC11×C25×C59 ⋊ C2
derived, SylowC11 ⋊ C2×C25×C59
HallC11×C59 ⋊ C2×C25
HallC11×C25 ⋊ C2×C59

Subgroups

subgroupG/H
center, hypercenterC25×C59D11
commutator, hypocenterC11C2×C25×C59
FrattiniC5C5×D11×C59
FittingC11×C25×C59C2
socleC5×C11×C59C2×C5
prime radicalC5×D11×C59C5
cosocleC5×C11C2×C5×C59
LCSG ▷ C11
UCSC1 ◁ C25×C59

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16225

Conjugacy classes & character table

10325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 4);