Finite Group Databasebeta

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C17×C3⋊#10596816 #44443856

order29580
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊#10596816
unambiguous semidirect productC3⋊(C17×#10596816)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C4
derived, HallC3×C5×C29 ⋊ C4×C17
HallC5×C17×C29 ⋊ Dic3
HallC3×C17×C29 ⋊ AGL(1,𝔽5)
HallC17×C29 ⋊ ΓL(1,𝔽16)
HallC3×C5×C17 ⋊ Dic29
HallC5×C29 ⋊ Dic3×C17
HallC3×C29 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ Dic87
HallC3×C17 ⋊ #10596816
SylowC29 ⋊ C17×ΓL(1,𝔽16)
HallC3×C5 ⋊ C17×Dic29
SylowC5 ⋊ C17×Dic87
SylowC3 ⋊ C17×#10596816

Subgroups

subgroupG/H
center, hypercenterC17C3⋊#10596816
commutator, hypocenterC3×C5×C29C4×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C29C4
prime radicalC3×D5×C17×C29C2
cosocleC3×D5×C29C2×C17
LCSG ▷ C3×C5×C29
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

3009 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29580, 68);