Finite Group Databasebeta

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C2×C7×D23×C11⋊C5 #47978428

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

Aliases

direct productC2×C7×D23×C11⋊C5
unambiguous semidirect productC23⋊(C22×C7×C11⋊C5)
unambiguous semidirect product(C2×C23)⋊(C2×C7×C11⋊C5)
unambiguous semidirect product(C2×C11×D23)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C11×D23)⋊C5

Splittings

Fitting, socleC2×C7×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C22×C5×C7
HallC7×C23×C11⋊C5 ⋊ C22
HallC2×C7×C11×D23 ⋊ C5
HallC7×C11×C23 ⋊ C22×C5
HallC23×C11⋊C5 ⋊ C22×C7
HallC2×C11×D23 ⋊ C5×C7
HallC7×C23 ⋊ C22×C11⋊C5
HallC7×C11 ⋊ C2×C5×D23
SylowC23 ⋊ C22×C7×C11⋊C5
SylowC11 ⋊ C2×C5×C7×D23

Subgroups

subgroupG/H
center, hypercenterC2×C7D23×C11⋊C5
commutator, cosocle, hypocenterC11×C23C22×C5×C7
FrattiniC1G
Fitting, socleC2×C7×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3542

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 62);