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C3×C7×D745 #44530971

order31290
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D745
unambiguous semidirect productC5⋊(C3×C7×D149)
unambiguous semidirect productC149⋊(C3×C7×D5)

Splittings

Fitting, socle, HallC3×C5×C7×C149 ⋊ C2
derived, HallC5×C149 ⋊ C2×C3×C7
HallC5×C7×C149 ⋊ C2×C3
HallC3×C7×C149 ⋊ D5
HallC3×C5×C149 ⋊ C2×C7
HallC7×C149 ⋊ C3×D5
HallC3×C149 ⋊ C7×D5
SylowC149 ⋊ C3×C7×D5
HallC3×C5×C7 ⋊ D149
HallC5×C7 ⋊ C3×D149
HallC3×C5 ⋊ C7×D149
SylowC5 ⋊ C3×C7×D149

Subgroups

subgroupG/H
center, hypercenterC3×C7D745
commutator, cosocle, hypocenterC5×C149C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C149C2
LCSG ▷ C5×C149
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15645

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31290, 7);