Finite Group Databasebeta

← Prev (#34089449) Next (#34089451) →

C3×C5×C7×Dic47 #34089450

order19740
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×Dic47
unambiguous semidirect productC47⋊(C3×C4×C5×C7)

Splittings

derived, SylowC47 ⋊ C3×C4×C5×C7
HallC3×C5×C7×C47 ⋊ C4
HallC5×C7×C47 ⋊ C3×C4
HallC3×C7×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ C4×C7
HallC7×C47 ⋊ C3×C4×C5
HallC5×C47 ⋊ C3×C4×C7
HallC3×C47 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D47
commutator, hypocenterC47C3×C4×C5×C7
FrattiniC2C3×C5×C7×D47
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C47C2×C3×C5×C7
LCSG ▷ C47
UCSC1 ◁ C2×C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

5250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 3);