Finite Group Databasebeta

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C2×C5×C7×D253 #47978479

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

Aliases

direct productC2×C5×C7×D253
unambiguous semidirect product(C2×C23)⋊(C5×C7×D11)

Splittings

Fitting, socleC2×C5×C7×C11×C23 ⋊ C2
derived, HallC11×C23 ⋊ C22×C5×C7
HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C22×C5
HallC5×C11×C23 ⋊ C22×C7
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC7×C23 ⋊ C2×C5×D11
HallC5×C23 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×C5×D23
HallC5×C11 ⋊ C2×C7×D23
SylowC23 ⋊ C2×C5×C7×D11
SylowC11 ⋊ C2×C5×C7×D23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D253
commutator, cosocle, hypocenterC11×C23C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C23C2
LCSG ▷ C11×C23
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17710

Conjugacy classes & character table

8960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 113);