Finite Group Databasebeta

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C5×C23×C22⋊(C19⋊C3) #39910798

order26220
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC5×C23×C22⋊(C19⋊C3)
unambiguous semidirect productC22⋊(C5×C23×C19⋊C3)
unambiguous semidirect productC19⋊(C5×A4×C23)
unambiguous semidirect product(C22×C5)⋊(C23×C19⋊C3)
unambiguous semidirect product(C22×C23)⋊(C5×C19⋊C3)
unambiguous semidirect product(C5×C19)⋊(A4×C23)
unambiguous semidirect product(C19×C23)⋊(C5×A4)
unambiguous semidirect product(C22×C5×C23)⋊(C19⋊C3)
unambiguous semidirect product(C5×C19×C23)⋊A4

Splittings

Fitting, socle, HallC22×C5×C19×C23 ⋊ C3
derived, HallC22×C19 ⋊ C3×C5×C23
HallC5×C19×C23 ⋊ A4
HallC22×C19×C23 ⋊ C3×C5
HallC22×C5×C23 ⋊ C19⋊C3
HallC19×C23 ⋊ C5×A4
HallC22×C5×C19 ⋊ C3×C23
HallC5×C19 ⋊ A4×C23
HallC22×C23 ⋊ C5×C19⋊C3
HallC22×C5 ⋊ C23×C19⋊C3
SylowC19 ⋊ C5×A4×C23
SylowC22 ⋊ C5×C23×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C23C22⋊(C19⋊C3)
commutator, cosocle, hypocenterC22×C19C3×C5×C23
FrattiniC1G
Fitting, socleC22×C5×C19×C23C3
LCSG ▷ C22×C19
UCSC1 ◁ C5×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8740

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 88);