Finite Group Databasebeta

← Prev (#39910807) Next (#39910809) →

C2×C5×C19×D69 #39910808

order26220
automorphism?
homologyAbelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C19×D69
unambiguous semidirect product(C2×C3)⋊(C5×C19×D23)
unambiguous semidirect product(C2×C23)⋊(C5×D3×C19)

Splittings

Fitting, socleC2×C3×C5×C19×C23 ⋊ C2
derived, HallC3×C23 ⋊ C22×C5×C19
HallC3×C5×C19×C23 ⋊ C22
HallC5×C19×C23 ⋊ C2×D3
HallC3×C19×C23 ⋊ C22×C5
HallC19×C23 ⋊ C2×C5×D3
HallC3×C5×C23 ⋊ C22×C19
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ C2×D3×C19
HallC3×C19 ⋊ C2×C5×D23
SylowC23 ⋊ C2×C5×D3×C19
HallC3×C5 ⋊ C2×C19×D23
SylowC3 ⋊ C2×C5×C19×D23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19D69
commutator, cosocle, hypocenterC3×C23C22×C5×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C19×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C2×C5×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13110

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 98);