Finite Group Databasebeta

← Prev (#44501268) Next (#44501270) →

C5×#20259493 #44501269

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#20259493

Splittings

derived, HallC7×C73 ⋊ C3×C4×C5
HallC5×Dic511 ⋊ C3
HallC5×#13095276 ⋊ C4
HallC5×C7×C73 ⋊ C3×C4
HallDic511 ⋊ C3×C5
Hall#13095276 ⋊ C4×C5
HallC5×C73 ⋊ ΓL(1,𝔽8)⋊C4
SylowC73 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ Dic73⋊C3
SylowC7 ⋊ C5×Dic73⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#15690450
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC2C5×#15690450
Fitting, socleC2×C5×C7×C73C2×C3
prime radicalC2×C5×#13095276C2
cosocleC2×C7×C73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 32);