Finite Group Databasebeta

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C5×D57⋊D23 #39910770

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

Aliases

direct productC5×D57⋊D23
unambiguous semidirect productD57⋊(C5×D23)
unambiguous semidirect productD69⋊(C5×D19)
unambiguous semidirect productD437⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C19×C23 ⋊ C22
derived, HallC3×C19×C23 ⋊ C22×C5
HallC5×C19×C23 ⋊ C2×D3
HallC19×C23 ⋊ C2×C5×D3
HallC3×C5×C23 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ D3×D19
HallC5×C19 ⋊ D3×D23
HallC3×C23 ⋊ C2×C5×D19
HallC3×C19 ⋊ C2×C5×D23
SylowC23 ⋊ C5×D3×D19
SylowC19 ⋊ C5×D3×D23
HallC3×C5 ⋊ D19×D23
SylowC3 ⋊ C5×D19×D23

Subgroups

subgroupG/H
center, hypercenterC5D57⋊D23
commutator, cosocle, hypocenterC3×C19×C23C22×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C23C22
LCSG ▷ C3×C19×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 60);