Finite Group Databasebeta

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C3×C5×C7×D167 #46856376

order35070
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×D167
unambiguous semidirect productC167⋊(C2×C3×C5×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C167 ⋊ C2
derived, SylowC167 ⋊ C2×C3×C5×C7
HallC5×C7×C167 ⋊ C2×C3
HallC3×C7×C167 ⋊ C2×C5
HallC3×C5×C167 ⋊ C2×C7
HallC7×C167 ⋊ C2×C3×C5
HallC5×C167 ⋊ C2×C3×C7
HallC3×C167 ⋊ C2×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7D167
commutator, cosocle, hypocenterC167C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C167C2
LCSG ▷ C167
UCSC1 ◁ C3×C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17535

Conjugacy classes & character table

8925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35070, 3);