Finite Group Databasebeta

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C2×D7×C23×C11⋊C5 #47978431

order35420
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×D7×C23×C11⋊C5
unambiguous semidirect productC7⋊(C22×C23×C11⋊C5)
unambiguous semidirect product(C2×C7)⋊(C2×C23×C11⋊C5)
unambiguous semidirect product(C2×C11×D7)⋊(C5×C23)
unambiguous semidirect product(C2×C11×D7×C23)⋊C5

Splittings

Fitting, socleC2×C7×C11×C23 ⋊ C2×C5
derived, HallC7×C11 ⋊ C22×C5×C23
HallC7×C23×C11⋊C5 ⋊ C22
HallC2×C11×D7×C23 ⋊ C5
HallC7×C11×C23 ⋊ C22×C5
HallC7×C11⋊C5 ⋊ C22×C23
HallC2×C11×D7 ⋊ C5×C23
HallC11×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D7×C23
SylowC7 ⋊ C22×C23×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C23D7×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C5×C23
FrattiniC1G
Fitting, socleC2×C7×C11×C23C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3542

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 65);