Finite Group Databasebeta

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C2×C5×C23⋊(D19⋊C3) #39910748

order26220
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C23⋊(D19⋊C3)
unambiguous semidirect product(C2×C23)⋊(C5×D19⋊C3)
unambiguous semidirect product(C2×C19⋊C3)⋊(C5×D23)
unambiguous semidirect product(C2×D437)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D437)⋊C3

Splittings

Fitting, socleC2×C5×C19×C23 ⋊ C2×C3
derived, HallC19×C23 ⋊ C22×C3×C5
HallC2×C5×D437 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C22
HallC5×C19×C23 ⋊ C22×C3
HallC2×D437 ⋊ C3×C5
HallC23×C19⋊C3 ⋊ C22×C5
HallC5×C19⋊C3 ⋊ C2×D23
HallC5×C23 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D23
HallC19⋊C3 ⋊ C2×C5×D23
SylowC23 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C2×C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC2×C5C23⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C23C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C19×C23C2×C3
LCSG ▷ C19×C23
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4370

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 38);