Finite Group Databasebeta

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C19×D15×D23 #39910775

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

Aliases

direct productC19×D15×D23
unambiguous semidirect product(C3×D23)⋊(D5×C19)
unambiguous semidirect product(C5×D23)⋊(D3×C19)

Splittings

Fitting, socle, HallC3×C5×C19×C23 ⋊ C22
derived, HallC3×C5×C23 ⋊ C22×C19
HallC5×C19×C23 ⋊ C2×D3
HallC3×C19×C23 ⋊ C2×D5
HallC19×C23 ⋊ C2×D15
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ C2×D3×C19
HallC5×C19 ⋊ D3×D23
HallC3×C23 ⋊ C2×D5×C19
HallC3×C19 ⋊ D5×D23
SylowC23 ⋊ C2×C19×D15
HallC3×C5 ⋊ C2×C19×D23
SylowC5 ⋊ D3×C19×D23
SylowC3 ⋊ D5×C19×D23

Subgroups

subgroupG/H
center, hypercenterC19D15×D23
commutator, cosocle, hypocenterC3×C5×C23C22×C19
FrattiniC1G
Fitting, socleC3×C5×C19×C23C22
LCSG ▷ C3×C5×C23
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Conjugacy classes & character table

2223 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 65);