Finite Group Databasebeta

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C4×C7×C23×C11⋊C5 #47978369

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C23×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C7×C23)
unambiguous semidirect product(C4×C7×C11)⋊(C5×C23)
unambiguous semidirect product(C4×C11×C23)⋊(C5×C7)
unambiguous semidirect product(C4×C7×C11×C23)⋊C5

Splittings

Fitting, HallC4×C7×C11×C23 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C7×C23
HallC7×C11×C23 ⋊ C4×C5
HallC4×C11×C23 ⋊ C5×C7
HallC4×C7×C11 ⋊ C5×C23
HallC11×C23 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5×C23
HallC4×C11 ⋊ C5×C7×C23

Subgroups

subgroupG/H
center, hypercenterC4×C7×C23C11⋊C5
commutator, hypocenterC11C4×C5×C7×C23
FrattiniC2C2×C7×C23×C11⋊C5
FittingC4×C7×C11×C23C5
socleC2×C7×C11×C23C2×C5
prime radicalC2×C7×C23×C11⋊C5C2
cosocleC2×C11C2×C5×C7×C23
LCSG ▷ C11
UCSC1 ◁ C4×C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7084

Conjugacy classes & character table

4508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 3);