Finite Group Databasebeta

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C52×A4×C19⋊C3 #30685819

order17100
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC52×A4×C19⋊C3
unambiguous semidirect product(C22×C19⋊C3)⋊(C3×C52)
unambiguous semidirect product(A4×C19)⋊(C3×C52)
unambiguous semidirect product(C22⋊(C19⋊C3))⋊(C3×C52)
unambiguous semidirect product(C22×C5×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C5×A4×C19)⋊(C3×C5)
unambiguous semidirect product(C5×C22⋊(C19⋊C3))⋊(C3×C5)

Splittings

Fitting, socle, HallC22×C52×C19 ⋊ C32
derived, HallC22×C19 ⋊ C32×C52
HallC52×C19 ⋊ C3×A4
HallC22×C52 ⋊ C3×C19⋊C3
SylowC19 ⋊ C3×C52×A4
SylowC22 ⋊ C3×C52×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC52A4×C19⋊C3
commutator, cosocle, hypocenterC22×C19C32×C52
FrattiniC1G
Fitting, socleC22×C52×C19C32
LCSG ▷ C22×C19
UCSC1 ◁ C52

224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1900

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 456);