Finite Group Databasebeta

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C2×C32×D715 #38788307

order25740
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D715
unambiguous semidirect product(C2×C5)⋊(C32×D143)
unambiguous semidirect product(C2×C11)⋊(C32×D65)

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derived, HallC5×C11×C13 ⋊ C22×C32
HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D5
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C32×D5
HallC32×C13 ⋊ C2×D55
HallC32×C11 ⋊ C2×D65
HallC5×C13 ⋊ C2×C32×D11
HallC5×C11 ⋊ C2×C32×D13
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ C2×C32×D55
SylowC11 ⋊ C2×C32×D65
SylowC5 ⋊ C2×C32×D143

Subgroups

subgroupG/H
center, hypercenterC2×C32D715
commutator, cosocle, hypocenterC5×C11×C13C22×C32
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C2×C32

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12870

Conjugacy classes & character table

6462 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 538);