Finite Group Databasebeta

← Prev (#44447133) Next (#44447135) →

C3×C5×Dic71⋊C7 #44447134

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic71⋊C7
unambiguous semidirect product(C5×Dic71)⋊(C3×C7)
unambiguous semidirect product(C3×C5×Dic71)⋊C7

Splittings

derived, SylowC71 ⋊ C3×C4×C5×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallC3×C5×Dic71 ⋊ C7
HallC5×C71⋊C7 ⋊ C3×C4
HallC3×C71⋊C7 ⋊ C4×C5
HallC5×Dic71 ⋊ C3×C7
HallC3×C5×C71 ⋊ C4×C7
HallC3×Dic71 ⋊ C5×C7
HallC71⋊C7 ⋊ C3×C4×C5
HallC5×C71 ⋊ C3×C4×C7
HallDic71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D71⋊C7
commutator, hypocenterC71C3×C4×C5×C7
FrattiniC2C3×C5×D71⋊C7
Fitting, socleC2×C3×C5×C71C2×C7
prime radicalC2×C3×C5×C71⋊C7C2
cosocleC2×C71C2×C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4260

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 22);