Finite Group Databasebeta

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C3×C52×(C19⋊C3)⋊C4 #30685646

order17100
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C52×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C3×C4×C52)
unambiguous semidirect productDic19⋊(C32×C52)
unambiguous semidirect product(C3×Dic19)⋊(C3×C52)
unambiguous semidirect product(C5×Dic19)⋊(C32×C5)
unambiguous semidirect product(C3×C5×Dic19)⋊(C3×C5)

Splittings

derived, SylowC19 ⋊ C32×C4×C52
HallC3×C52×C19⋊C3 ⋊ C4
HallC52×Dic19 ⋊ C32
HallC52×C19 ⋊ C32×C4
HallC3×C19⋊C3 ⋊ C4×C52
HallDic19 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D19⋊C3
commutator, hypocenterC19C32×C4×C52
FrattiniC2C3×C52×D19⋊C3
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C52×C19⋊C3C2
cosocleC2×C19C2×C32×C52
LCSG ▷ C19
UCSC1 ◁ C2×C3×C52

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5700

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 283);