Finite Group Databasebeta

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C3×C7×C13×#595 #32915559

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×#595

Splittings

Fitting, socle, HallC3×C7×C13×C17 ⋊ C4
derived, SylowC17 ⋊ C3×C4×C7×C13
HallC7×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ C4×C13
HallC13×C17 ⋊ C3×C4×C7
HallC7×C17 ⋊ C3×C4×C13
HallC3×C17 ⋊ C4×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13#595
commutator, hypocenterC17C3×C4×C7×C13
FrattiniC1G
Fitting, socleC3×C7×C13×C17C4
prime radicalC3×C7×C13×D17C2
cosocleD17C2×C3×C7×C13
LCSG ▷ C17
UCSC1 ◁ C3×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4641

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 154);