Finite Group Databasebeta

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C5×C23⋊(D49⋊C3) #46798916

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23⋊(D49⋊C3)
unambiguous semidirect productC23⋊(C5×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(C5×D23)
unambiguous semidirect productD1127⋊(C3×C5)
unambiguous semidirect product(C5×D1127)⋊C3

Splittings

Fitting, HallC5×C23×C49 ⋊ C2×C3
derived, HallC23×C49 ⋊ C2×C3×C5
HallC5×C23×C49⋊C3 ⋊ C2
HallC5×D1127 ⋊ C3
HallC23×C49⋊C3 ⋊ C2×C5
HallD1127 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ D23
HallC5×C49 ⋊ C3×D23
HallC49⋊C3 ⋊ C5×D23
HallC5×C23 ⋊ D49⋊C3
SylowC49 ⋊ C3×C5×D23
SylowC23 ⋊ C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C23⋊(D49⋊C3)
commutator, cosocle, hypocenterC23×C49C2×C3×C5
FrattiniC7C5×ΓL(1,𝔽8)⋊D23
FittingC5×C23×C49C2×C3
socleC5×C7×C23AGL(1,𝔽7)
LCSG ▷ C23×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5635

Conjugacy classes & character table

1115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 20);