Finite Group Databasebeta

← Prev (#44544972) Next (#44544974) →

D3×C11⋊C5×C97 #44544973

order32010
automorphism?
homologyAbelianization (H1) = C2×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11⋊C5×C97
unambiguous semidirect productC3⋊(C2×C11⋊C5×C97)
unambiguous semidirect product(D3×C11)⋊(C5×C97)
unambiguous semidirect product(D3×C11×C97)⋊C5

Splittings

Fitting, socle, HallC3×C11×C97 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C97
HallC3×C11⋊C5×C97 ⋊ C2
HallD3×C11×C97 ⋊ C5
HallC11×C97 ⋊ C5×D3
HallC3×C97 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ C2×C97
HallD3×C11 ⋊ C5×C97
SylowC11 ⋊ C5×D3×C97
SylowC3 ⋊ C2×C11⋊C5×C97

Subgroups

subgroupG/H
center, hypercenterC97D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C97
FrattiniC1G
Fitting, socleC3×C11×C97C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3201

Conjugacy classes & character table

2037 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 23);