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C3×(C19⋊C3)⋊#1039 #30685649

order17100
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×(C19⋊C3)⋊#1039
unambiguous semidirect product(C19⋊C3)⋊(C3×#1039)

Splittings

derived, HallC52×C19 ⋊ C32×C4
HallC3×C52×C19⋊C3 ⋊ C4
HallC19⋊#1039 ⋊ C32
HallC3×C19⋊C3 ⋊ #1039
SylowC52 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(C5⋊(D19⋊C3))
commutator, hypocenterC52×C19C32×C4
FrattiniC2C3×C5⋊(C5⋊(D19⋊C3))
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C52×C19⋊C3C2
cosocleC2×C52×C19C2×C32
LCSG ▷ C52×C19
UCSC1 ◁ C2×C3

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5700

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 286);