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C7×D2265 #44540254

order31710
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2265
unambiguous semidirect productC3⋊(C7×D755)
unambiguous semidirect productC5⋊(C7×D453)
unambiguous semidirect productC151⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C151 ⋊ C2
derived, HallC3×C5×C151 ⋊ C2×C7
HallC5×C7×C151 ⋊ D3
HallC3×C7×C151 ⋊ D5
HallC7×C151 ⋊ D15
HallC5×C151 ⋊ D3×C7
HallC3×C151 ⋊ C7×D5
SylowC151 ⋊ C7×D15
HallC3×C5×C7 ⋊ D151
HallC5×C7 ⋊ D453
HallC3×C7 ⋊ D755
HallC3×C5 ⋊ C7×D151
SylowC5 ⋊ C7×D453
SylowC3 ⋊ C7×D755

Subgroups

subgroupG/H
center, hypercenterC7D2265
commutator, cosocle, hypocenterC3×C5×C151C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C151C2
LCSG ▷ C3×C5×C151
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15855

Conjugacy classes & character table

7938 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 23);