Finite Group Databasebeta

← Prev (#29506874) Next (#29506876) →

C2×C3×C7×D61⋊C3 #29506875

order15372
isoclinismisoclinic class of D61⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C7×D61⋊C3
unambiguous semidirect productD61⋊(C2×C32×C7)
unambiguous semidirect product(C61⋊C3)⋊(C22×C3×C7)
unambiguous semidirect product(C2×D61)⋊(C32×C7)
unambiguous semidirect product(C2×C61⋊C3)⋊(C2×C3×C7)
unambiguous semidirect product(C2×C3×D61)⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C7×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C22×C32×C7
HallC3×C7×C61⋊C3 ⋊ C22
HallC2×C7×D61 ⋊ C32
HallC3×C61⋊C3 ⋊ C22×C7
HallC7×C61 ⋊ C22×C32
HallC2×D61 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D61⋊C3
commutator, cosocle, hypocenterC61C22×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C2×C3×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2562

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 185);