Finite Group Databasebeta

← Prev (#44501397) Next (#44501399) →

C3×C73×C7⋊AGL(1,𝔽5) #44501398

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1

Aliases

direct productC3×C73×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C4
derived, HallC5×C7 ⋊ C3×C4×C73
HallC5×C7×C73 ⋊ C3×C4
HallC3×C7×C73 ⋊ AGL(1,𝔽5)
HallC3×C5×C73 ⋊ Dic7
HallC7×C73 ⋊ C3×AGL(1,𝔽5)
HallC5×C73 ⋊ C3×Dic7
HallC3×C5×C7 ⋊ C4×C73
HallC3×C7 ⋊ AGL(1,𝔽5)×C73
HallC3×C5 ⋊ Dic7×C73
SylowC7 ⋊ C3×AGL(1,𝔽5)×C73
SylowC5 ⋊ C3×Dic7×C73

Subgroups

subgroupG/H
center, hypercenterC3×C73C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C73
FrattiniC1G
Fitting, socleC3×C5×C7×C73C4
prime radicalC3×C7×D5×C73C2
cosocleC7×D5C2×C3×C73
LCSG ▷ C5×C7
UCSC1 ◁ C3×C73

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

3723 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 161);