Finite Group Databasebeta

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C7×#11725133⋊C3 #32915459

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

Aliases

direct productC7×#11725133⋊C3
unambiguous semidirect product#11725133⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C3×C4
derived, HallC13×C17 ⋊ C3×C4×C7
HallC7×#11725133 ⋊ C3
HallC7×C17×C13⋊C3 ⋊ C4
Hall#11725133 ⋊ C3×C7
HallC17×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ #595
HallC7×C17 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×#595
HallC13⋊C3 ⋊ C7×#595
SylowC17 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×C7×#595

Subgroups

subgroupG/H
center, hypercenterC7#11725133⋊C3
commutator, hypocenterC13×C17C3×C4×C7
FrattiniC1G
Fitting, socleC7×C13×C17C3×C4
prime radicalC7×D17×C13⋊C3C2
cosocleC13×D17C2×C3×C7
LCSG ▷ C13×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1547

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 54);