Finite Group Databasebeta

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C17×Dic5×C19⋊C3 #34084309

order19380
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic5×C19⋊C3
unambiguous semidirect product(C19×Dic5)⋊(C3×C17)
unambiguous semidirect product(C17×C19×Dic5)⋊C3

Splittings

derived, HallC5×C19 ⋊ C3×C4×C17
HallC17×C19×Dic5 ⋊ C3
HallC5×C17×C19⋊C3 ⋊ C4
HallC5×C17×C19 ⋊ C3×C4
HallC19×Dic5 ⋊ C3×C17
HallC17×C19 ⋊ C3×Dic5
HallC5×C19⋊C3 ⋊ C4×C17
HallC5×C17 ⋊ C4×C19⋊C3
SylowC19 ⋊ C3×C17×Dic5
SylowC5 ⋊ C4×C17×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C17D5×C19⋊C3
commutator, hypocenterC5×C19C3×C4×C17
FrattiniC2D5×C17×C19⋊C3
Fitting, socleC2×C5×C17×C19C2×C3
prime radicalC2×C5×C17×C19⋊C3C2
cosocleC2×C5×C19C2×C3×C17
LCSG ▷ C5×C19
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6460

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 21);