Finite Group Databasebeta

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C5×C7×D489 #46803832

order34230
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D489
unambiguous semidirect productC3⋊(C5×C7×D163)
unambiguous semidirect productC163⋊(C5×D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C163 ⋊ C2
derived, HallC3×C163 ⋊ C2×C5×C7
HallC5×C7×C163 ⋊ D3
HallC3×C7×C163 ⋊ C2×C5
HallC3×C5×C163 ⋊ C2×C7
HallC7×C163 ⋊ C5×D3
HallC5×C163 ⋊ D3×C7
SylowC163 ⋊ C5×D3×C7
HallC3×C5×C7 ⋊ D163
HallC3×C7 ⋊ C5×D163
HallC3×C5 ⋊ C7×D163
SylowC3 ⋊ C5×C7×D163

Subgroups

subgroupG/H
center, hypercenterC5×C7D489
commutator, cosocle, hypocenterC3×C163C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C163C2
LCSG ▷ C3×C163
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17115

Conjugacy classes & character table

8610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34230, 14);