Finite Group Databasebeta

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C3×C49×D115 #46798903

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×D115
unambiguous semidirect productC5⋊(C3×D23×C49)
unambiguous semidirect productC23⋊(C3×D5×C49)

Splittings

Fitting, HallC3×C5×C23×C49 ⋊ C2
derived, HallC5×C23 ⋊ C2×C3×C49
HallC5×C23×C49 ⋊ C2×C3
HallC3×C23×C49 ⋊ D5
HallC23×C49 ⋊ C3×D5
HallC3×C5×C49 ⋊ D23
HallC3×C5×C23 ⋊ C2×C49
HallC5×C49 ⋊ C3×D23
HallC3×C23 ⋊ D5×C49
SylowC23 ⋊ C3×D5×C49
HallC3×C5 ⋊ D23×C49
SylowC5 ⋊ C3×D23×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49D115
commutator, hypocenterC5×C23C2×C3×C49
FrattiniC7C3×C7×D115
FittingC3×C5×C23×C49C2
socleC3×C5×C7×C23C2×C7
prime radicalC3×C7×D115C7
cosocleC5×C7×C23C2×C3×C7
LCSG ▷ C5×C23
UCSC1 ◁ C3×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

8673 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 7);