Finite Group Databasebeta

← Prev (#30685520) Next (#30685522) →

C22×C3×C25×C19⋊C3 #30685521

order17100
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C25×C19⋊C3

Splittings

FittingC22×C3×C19×C25 ⋊ C3
derived, SylowC19 ⋊ C22×C32×C25
HallC22×C19×C25 ⋊ C32
HallC19×C25 ⋊ C22×C32
HallC22×C19 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC22×C3×C25C19⋊C3
commutator, hypocenterC19C22×C32×C25
FrattiniC5C22×C3×C5×C19⋊C3
FittingC22×C3×C19×C25C3
socleC22×C3×C5×C19C3×C5
prime radicalC22×C3×C5×C19⋊C3C5
cosocleC5×C19C22×C32×C5
LCSG ▷ C19
UCSC1 ◁ C22×C3×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5700

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 158);