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C5×(C19⋊C3)⋊Dic17 #34084308

order19380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C19⋊C3)⋊Dic17
unambiguous semidirect product(C19⋊C3)⋊(C5×Dic17)
unambiguous semidirect productDic323⋊(C3×C5)
unambiguous semidirect product(C5×Dic323)⋊C3

Splittings

derived, HallC17×C19 ⋊ C3×C4×C5
HallC5×Dic323 ⋊ C3
HallC5×C17×C19⋊C3 ⋊ C4
HallC5×C17×C19 ⋊ C3×C4
HallDic323 ⋊ C3×C5
HallC17×C19⋊C3 ⋊ C4×C5
HallC5×C19⋊C3 ⋊ Dic17
HallC5×C19 ⋊ C3×Dic17
HallC5×C17 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ C5×Dic17
SylowC19 ⋊ C3×C5×Dic17
SylowC17 ⋊ C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C17⋊(D19⋊C3)
commutator, hypocenterC17×C19C3×C4×C5
FrattiniC2C5×C17⋊(D19⋊C3)
Fitting, socleC2×C5×C17×C19C2×C3
prime radicalC2×C5×C17×C19⋊C3C2
cosocleC2×C17×C19C2×C3×C5
LCSG ▷ C17×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 20);