Finite Group Databasebeta

← Prev (#44570069) Next (#44570071) →

C3×C5×C7×C103⋊C3 #44570070

order32445
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×C103⋊C3
unambiguous semidirect productC103⋊(C32×C5×C7)
unambiguous semidirect product(C3×C103)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C103)⋊(C32×C7)
unambiguous semidirect product(C3×C5×C103)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C103 ⋊ C3
derived, SylowC103 ⋊ C32×C5×C7
HallC5×C7×C103 ⋊ C32
HallC7×C103 ⋊ C32×C5
HallC5×C103 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C103⋊C3
commutator, cosocle, hypocenterC103C32×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C103C3
LCSG ▷ C103
UCSC1 ◁ C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10815

Conjugacy classes & character table

3885 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32445, 8);