Finite Group Databasebeta

← Prev (#32915560) Next (#32915562) →

C3×C7×#11725130 #32915561

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×#11725130

Splittings

Fitting, socle, HallC3×C7×C13×C17 ⋊ C4
derived, HallC13×C17 ⋊ C3×C4×C7
HallC7×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ #261
HallC3×C7×C13 ⋊ #595
HallC7×C17 ⋊ C3×#261
HallC7×C13 ⋊ C3×#595
HallC3×C17 ⋊ C7×#261
HallC3×C13 ⋊ C7×#595
SylowC17 ⋊ C3×C7×#261
SylowC13 ⋊ C3×C7×#595

Subgroups

subgroupG/H
center, hypercenterC3×C7#11725130
commutator, hypocenterC13×C17C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C17C4
prime radicalC3×C7×D221C2
cosocleD221C2×C3×C7
LCSG ▷ C13×C17
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4641

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 156);