Finite Group Databasebeta

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C2×C11×D715 #44538288

order31460
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D715
unambiguous semidirect product(C2×C5)⋊(C11×D143)
unambiguous semidirect product(C2×C11)⋊(C11×D65)
unambiguous semidirect product(C2×C13)⋊(C11×D55)

Splittings

Fitting, socleC2×C5×C112×C13 ⋊ C2
derivedC5×C11×C13 ⋊ C22×C11
HallC5×C112×C13 ⋊ C22
HallC112×C13 ⋊ C2×D5
HallC5×C112 ⋊ C2×D13
SylowC112 ⋊ C2×D65
HallC5×C13 ⋊ C2×C11×D11
SylowC13 ⋊ C2×C11×D55
SylowC5 ⋊ C2×C11×D143

Subgroups

subgroupG/H
center, hypercenterC2×C11D715
commutator, cosocle, hypocenterC5×C11×C13C22×C11
FrattiniC1G
Fitting, socleC2×C5×C112×C13C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

7898 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 228);