Finite Group Databasebeta

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C3×C25×(C19⋊C3)⋊C4 #30685409

order17100
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×C25×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C3×C4×C25)
unambiguous semidirect productDic19⋊(C32×C25)
unambiguous semidirect product(C3×Dic19)⋊(C3×C25)
unambiguous semidirect product(C25×Dic19)⋊C32
unambiguous semidirect product(C3×C25×Dic19)⋊C3

Splittings

derived, SylowC19 ⋊ C32×C4×C25
HallC3×C25×C19⋊C3 ⋊ C4
HallC25×Dic19 ⋊ C32
HallC19×C25 ⋊ C32×C4
HallC3×C19⋊C3 ⋊ C4×C25
HallDic19 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D19⋊C3
commutator, hypocenterC19C32×C4×C25
FrattiniC2×C5C3×C5×D19⋊C3
FittingC2×C3×C19×C25C2×C3
socleC2×C3×C5×C19C2×C3×C5
prime radicalC2×C3×C5×C19⋊C3C2×C5
cosocleC2×C5×C19C2×C32×C5
LCSG ▷ C19
UCSC1 ◁ C2×C3×C25

108 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, 46);