Finite Group Databasebeta

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C5×D3×C23×D19 #39910767

order26220
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C23×D19
unambiguous semidirect product(D3×C19)⋊(C2×C5×C23)
unambiguous semidirect product(C3×D19)⋊(C2×C5×C23)
unambiguous semidirect productD57⋊(C2×C5×C23)

Splittings

Fitting, socle, HallC3×C5×C19×C23 ⋊ C22
derived, HallC3×C19 ⋊ C22×C5×C23
HallC5×C19×C23 ⋊ C2×D3
HallC3×C19×C23 ⋊ C22×C5
HallC19×C23 ⋊ C2×C5×D3
HallC3×C5×C23 ⋊ C2×D19
HallC3×C5×C19 ⋊ C22×C23
HallC5×C19 ⋊ C2×D3×C23
HallC3×C23 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C5×D3×C23
HallC3×C5 ⋊ C2×C23×D19
SylowC3 ⋊ C2×C5×C23×D19

Subgroups

subgroupG/H
center, hypercenterC5×C23D3×D19
commutator, cosocle, hypocenterC3×C19C22×C5×C23
FrattiniC1G
Fitting, socleC3×C5×C19×C23C22
LCSG ▷ C3×C19
UCSC1 ◁ C5×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Conjugacy classes & character table

3795 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 57);