Finite Group Databasebeta

← Prev (#45684457) Next (#45684459) →

D35×D79⋊C3 #45684458

order33180
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD35×D79⋊C3
unambiguous semidirect productD79⋊(C3×D35)
unambiguous semidirect product(C5×D79⋊C3)⋊D7
unambiguous semidirect product(C7×D79⋊C3)⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C79 ⋊ C22×C3
HallD35×D79 ⋊ C3
HallC5×C7×C79⋊C3 ⋊ C22
HallC7×C79⋊C3 ⋊ C2×D5
HallC5×C79⋊C3 ⋊ C2×D7
HallC7×C79 ⋊ C2×C3×D5
HallC5×C79 ⋊ C2×C3×D7
HallC79⋊C3 ⋊ C2×D35
SylowC79 ⋊ C2×C3×D35
HallC5×C7 ⋊ C2×D79⋊C3
SylowC7 ⋊ D5×D79⋊C3
SylowC5 ⋊ D7×D79⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C79C22×C3
LCSG ▷ C5×C7×C79
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 89);