Finite Group Databasebeta

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C2×C11×C23×D35 #47978488

order35420
automorphism?
homologyAbelianization (H1) = C22×C11×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C23×D35
unambiguous semidirect product(C2×C5)⋊(C11×D7×C23)
unambiguous semidirect product(C2×C7)⋊(D5×C11×C23)

Splittings

Fitting, socleC2×C5×C7×C11×C23 ⋊ C2
derived, HallC5×C7 ⋊ C22×C11×C23
HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C22×C11
HallC5×C7×C11 ⋊ C22×C23
HallC7×C23 ⋊ C2×D5×C11
HallC5×C23 ⋊ C2×C11×D7
HallC7×C11 ⋊ C2×D5×C23
HallC5×C11 ⋊ C2×D7×C23
SylowC7 ⋊ C2×D5×C11×C23
SylowC5 ⋊ C2×C11×D7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C11×C23D35
commutator, cosocle, hypocenterC5×C7C22×C11×C23
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C23C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C11×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17710

Conjugacy classes & character table

9614 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 122);