Finite Group Databasebeta

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C5×#13094090⋊C3 #36383100

order22620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#13094090⋊C3
unambiguous semidirect product#13094090⋊(C3×C5)
unambiguous semidirect product(C5×#13094090)⋊C3

Splittings

Fitting, socle, HallC5×C13×C29 ⋊ C3×C4
derived, HallC13×C29 ⋊ C3×C4×C5
HallC5×#13094090 ⋊ C3
HallC5×C29×C13⋊C3 ⋊ C4
Hall#13094090 ⋊ C3×C5
HallC29×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ #1181
HallC5×C29 ⋊ Dic13⋊C3
HallC5×C13 ⋊ C3×#1181
HallC13⋊C3 ⋊ C5×#1181
SylowC29 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C3×C5×#1181

Subgroups

subgroupG/H
center, hypercenterC5#13094090⋊C3
commutator, hypocenterC13×C29C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C29C3×C4
prime radicalC5×C13⋊C3×D29C2
cosocleC13×D29C2×C3×C5
LCSG ▷ C13×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 30);