Finite Group Databasebeta

← Prev (#45659279) Next (#45659281) →

C3×C7×C23⋊#595 #45659280

order32844
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C23⋊#595
unambiguous semidirect productC23⋊(C3×C7×#595)

Splittings

Fitting, socle, HallC3×C7×C17×C23 ⋊ C4
derived, HallC17×C23 ⋊ C3×C4×C7
HallC7×C17×C23 ⋊ C3×C4
HallC3×C17×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ #595
HallC3×C7×C17 ⋊ Dic23
HallC7×C23 ⋊ C3×#595
HallC7×C17 ⋊ C3×Dic23
HallC3×C23 ⋊ C7×#595
HallC3×C17 ⋊ C7×Dic23
SylowC23 ⋊ C3×C7×#595
SylowC17 ⋊ C3×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC3×C7C23⋊#595
commutator, hypocenterC17×C23C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C17×C23C4
prime radicalC3×C7×C23×D17C2
cosocleC23×D17C2×C3×C7
LCSG ▷ C17×C23
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8211

Conjugacy classes & character table

2478 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 45);