Finite Group Databasebeta

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C22×C5×C7×C23⋊C11 #47978425

order35420
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C7×C23⋊C11
unambiguous semidirect product(C22×C23)⋊(C5×C7×C11)
unambiguous semidirect product(C22×C5×C23)⋊(C7×C11)
unambiguous semidirect product(C22×C7×C23)⋊(C5×C11)
unambiguous semidirect product(C22×C5×C7×C23)⋊C11

Splittings

Fitting, socle, HallC22×C5×C7×C23 ⋊ C11
derived, SylowC23 ⋊ C22×C5×C7×C11
HallC5×C7×C23 ⋊ C22×C11
HallC22×C7×C23 ⋊ C5×C11
HallC22×C5×C23 ⋊ C7×C11
HallC7×C23 ⋊ C22×C5×C11
HallC5×C23 ⋊ C22×C7×C11
HallC22×C23 ⋊ C5×C7×C11

Subgroups

subgroupG/H
center, hypercenterC22×C5×C7C23⋊C11
commutator, cosocle, hypocenterC23C22×C5×C7×C11
FrattiniC1G
Fitting, socleC22×C5×C7×C23C11
LCSG ▷ C23
UCSC1 ◁ C22×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3220

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 59);