Finite Group Databasebeta

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C5×C49×D69 #46798907

order33810
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×C49×D69
unambiguous semidirect productC3⋊(C5×D23×C49)
unambiguous semidirect productC23⋊(C5×D3×C49)

Splittings

Fitting, HallC3×C5×C23×C49 ⋊ C2
derived, HallC3×C23 ⋊ C2×C5×C49
HallC5×C23×C49 ⋊ D3
HallC3×C23×C49 ⋊ C2×C5
HallC23×C49 ⋊ C5×D3
HallC3×C5×C49 ⋊ D23
HallC3×C5×C23 ⋊ C2×C49
HallC3×C49 ⋊ C5×D23
HallC5×C23 ⋊ D3×C49
SylowC23 ⋊ C5×D3×C49
HallC3×C5 ⋊ D23×C49
SylowC3 ⋊ C5×D23×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49D69
commutator, hypocenterC3×C23C2×C5×C49
FrattiniC7C5×C7×D69
FittingC3×C5×C23×C49C2
socleC3×C5×C7×C23C2×C7
prime radicalC5×C7×D69C7
cosocleC3×C7×C23C2×C5×C7
LCSG ▷ C3×C23
UCSC1 ◁ C5×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

8820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 11);