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C3×#21419471 #36383151

order22620
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#21419471

Splittings

Fitting, socle, HallC3×C5×C13×C29 ⋊ C4
derived, HallC5×C13×C29 ⋊ C3×C4
HallC3×C13×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ #261
HallC13×C29 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ #1181
HallC5×C29 ⋊ C3×#261
HallC3×C29 ⋊ #63122
HallC5×C13 ⋊ C3×#1181
HallC3×C13 ⋊ #10596815
SylowC29 ⋊ C3×#63122
HallC3×C5 ⋊ #13094088
SylowC13 ⋊ C3×#10596815
SylowC5 ⋊ C3×#13094088

Subgroups

subgroupG/H
center, hypercenterC3#21419471
commutator, hypocenterC5×C13×C29C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C29C4
prime radicalC3×D1885C2
cosocleD1885C2×C3
LCSG ▷ C5×C13×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 81);