Finite Group Databasebeta

← Prev (#32915559) Next (#32915561) →

C3×C7×C17×#261 #32915560

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C17×#261

Splittings

Fitting, socle, HallC3×C7×C13×C17 ⋊ C4
derived, SylowC13 ⋊ C3×C4×C7×C17
HallC7×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C13 ⋊ C4×C17
HallC13×C17 ⋊ C3×C4×C7
HallC7×C13 ⋊ C3×C4×C17
HallC3×C13 ⋊ C4×C7×C17

Subgroups

subgroupG/H
center, hypercenterC3×C7×C17#261
commutator, hypocenterC13C3×C4×C7×C17
FrattiniC1G
Fitting, socleC3×C7×C13×C17C4
prime radicalC3×C7×C17×D13C2
cosocleD13C2×C3×C7×C17
LCSG ▷ C13
UCSC1 ◁ C3×C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4641

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 155);