Finite Group Databasebeta

← Prev (#35229837) Next (#35229839) →

C11×C19×#1035 #35229838

order20900
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC11×C19×#1035

Splittings

Fitting, HallC11×C19×C25 ⋊ C4
derived, SylowC25 ⋊ C4×C11×C19
HallC19×C25 ⋊ C4×C11
HallC11×C25 ⋊ C4×C19

Subgroups

subgroupG/H
center, hypercenterC11×C19#1035
commutator, hypocenterC25C4×C11×C19
FrattiniC5C11×C19×AGL(1,𝔽5)
FittingC11×C19×C25C4
socleC5×C11×C19AGL(1,𝔽5)
prime radicalC11×C19×D25C2
cosocleD25C2×C11×C19
LCSG ▷ C25
UCSC1 ◁ C11×C19

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 20);