Finite Group Databasebeta

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C3×C17×#10596816 #44443816

order29580
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×#10596816

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C4
derived, HallC5×C29 ⋊ C3×C4×C17
HallC5×C17×C29 ⋊ C3×C4
HallC3×C17×C29 ⋊ AGL(1,𝔽5)
HallC17×C29 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C29 ⋊ C4×C17
HallC3×C5×C17 ⋊ Dic29
HallC3×C29 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ C3×Dic29
SylowC29 ⋊ C3×C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×Dic29
SylowC5 ⋊ C3×C17×Dic29

Subgroups

subgroupG/H
center, hypercenterC3×C17#10596816
commutator, hypocenterC5×C29C3×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C29C4
prime radicalC3×D5×C17×C29C2
cosocleD5×C29C2×C3×C17
LCSG ▷ C5×C29
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

3111 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29580, 28);