Finite Group Databasebeta

D11×C25×C53 #44415358

order29150
automorphism?
homologyAbelianization (H1) = C2×C25×C53 · Schur multiplier (H2) = C1

Aliases

direct productD11×C25×C53

Splittings

Fitting, HallC11×C25×C53 ⋊ C2
derived, SylowC11 ⋊ C2×C25×C53
HallC11×C53 ⋊ C2×C25
HallC11×C25 ⋊ C2×C53

Subgroups

subgroupG/H
center, hypercenterC25×C53D11
commutator, hypocenterC11C2×C25×C53
FrattiniC5C5×D11×C53
FittingC11×C25×C53C2
socleC5×C11×C53C2×C5
prime radicalC5×D11×C53C5
cosocleC5×C11C2×C5×C53
LCSG ▷ C11
UCSC1 ◁ C25×C53

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14575

Conjugacy classes & character table

9275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29150, 4);