Finite Group Databasebeta

← Prev (#45684450) Next (#45684452) →

D5×#15693303 #45684451

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

Aliases

direct productD5×#15693303

Splittings

Fitting, socle, derived, HallC5×C7×C79 ⋊ C22×C3
HallD5×D7×C79 ⋊ C3
HallC5×#13110306 ⋊ C22
Hall#13110306 ⋊ C2×D5
HallC7×C79 ⋊ C2×C3×D5
HallC5×C79 ⋊ C2×AGL(1,𝔽7)
HallD5×D7 ⋊ C79⋊C3
SylowC79 ⋊ D5×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C79⋊C3
SylowC7 ⋊ C2×D5×C79⋊C3
SylowC5 ⋊ C2×#15693303

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 82);