Finite Group Databasebeta

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C5×C7×D483 #46798980

order33810
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D483
unambiguous semidirect productC3⋊(C5×C7×D161)
unambiguous semidirect productC7⋊(C5×C7×D69)
unambiguous semidirect productC23⋊(C5×C7×D21)

Splittings

Fitting, socle, HallC3×C5×C72×C23 ⋊ C2
derivedC3×C7×C23 ⋊ C2×C5×C7
HallC5×C72×C23 ⋊ D3
HallC3×C72×C23 ⋊ C2×C5
HallC72×C23 ⋊ C5×D3
HallC3×C5×C72 ⋊ D23
HallC3×C5×C23 ⋊ C7×D7
HallC5×C72 ⋊ D69
HallC3×C72 ⋊ C5×D23
HallC5×C23 ⋊ C7×D21
HallC3×C23 ⋊ C5×C7×D7
SylowC72 ⋊ C5×D69
SylowC23 ⋊ C5×C7×D21
HallC3×C5 ⋊ C7×D161
SylowC3 ⋊ C5×C7×D161

Subgroups

subgroupG/H
center, hypercenterC5×C7D483
commutator, cosocle, hypocenterC3×C7×C23C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C3×C7×C23
UCSC1 ◁ C5×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

8505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 84);