Finite Group Databasebeta

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C4×C5×C17×C11⋊C5 #34035170

order18700
automorphism?
homologyAbelianization (H1) = C4×C52×C17 · Schur multiplier (H2) = C5

Aliases

direct productC4×C5×C17×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C52×C17)
unambiguous semidirect product(C4×C5×C11)⋊(C5×C17)
unambiguous semidirect product(C4×C11×C17)⋊C52
unambiguous semidirect product(C4×C5×C11×C17)⋊C5

Splittings

FittingC4×C5×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C4×C52×C17
HallC4×C11×C17 ⋊ C52
HallC11×C17 ⋊ C4×C52
HallC4×C11 ⋊ C52×C17

Subgroups

subgroupG/H
center, hypercenterC4×C5×C17C11⋊C5
commutator, hypocenterC11C4×C52×C17
FrattiniC2C2×C5×C17×C11⋊C5
FittingC4×C5×C11×C17C5
socleC2×C5×C11×C17C2×C5
prime radicalC2×C5×C17×C11⋊C5C2
cosocleC2×C11C2×C52×C17
LCSG ▷ C11
UCSC1 ◁ C4×C5×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3740

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 55);