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D7×D1065 #44447252

order29820
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD7×D1065
unambiguous semidirect product(C3×D7)⋊D355
unambiguous semidirect product(C5×D7)⋊D213
unambiguous semidirect product(D7×C71)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C2×D3
HallC3×C7×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C2×D7
HallC7×C71 ⋊ C2×D15
HallC5×C71 ⋊ D3×D7
HallC3×C71 ⋊ D5×D7
HallC3×C5×C7 ⋊ C2×D71
SylowC71 ⋊ D7×D15
HallC5×C7 ⋊ C2×D213
HallC3×C7 ⋊ C2×D355
HallC3×C5 ⋊ D7×D71
SylowC7 ⋊ C2×D1065
SylowC5 ⋊ D7×D213
SylowC3 ⋊ D7×D355

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C71C22
LCSG ▷ C3×C5×C7×C71
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7455

Conjugacy classes & character table

2670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 140);