Finite Group Databasebeta

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C3×C4×C5×C7×C11⋊C5 #37528381

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C4×C5×C7×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C3×C52×C7)
unambiguous semidirect product(C3×C4×C11)⋊(C52×C7)
unambiguous semidirect product(C4×C5×C11)⋊(C3×C5×C7)
unambiguous semidirect product(C3×C4×C5×C11)⋊(C5×C7)
unambiguous semidirect product(C3×C4×C7×C11)⋊C52
unambiguous semidirect product(C3×C4×C5×C7×C11)⋊C5

Splittings

FittingC3×C4×C5×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C3×C4×C52×C7
HallC3×C4×C7×C11 ⋊ C52
HallC4×C7×C11 ⋊ C3×C52
HallC3×C7×C11 ⋊ C4×C52
HallC3×C4×C11 ⋊ C52×C7
HallC7×C11 ⋊ C3×C4×C52
HallC4×C11 ⋊ C3×C52×C7
HallC3×C11 ⋊ C4×C52×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C7C11⋊C5
commutator, hypocenterC11C3×C4×C52×C7
FrattiniC2C2×C3×C5×C7×C11⋊C5
FittingC3×C4×C5×C7×C11C5
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C11C2×C3×C52×C7
LCSG ▷ C11
UCSC1 ◁ C3×C4×C5×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 192);