Finite Group Databasebeta

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C23×C3⋊(C7⋊#595) #45659299

order32844
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(C7⋊#595)
unambiguous semidirect productC3⋊(C23×C7⋊#595)
unambiguous semidirect productC7⋊(C23×C3⋊#595)

Splittings

Fitting, socle, HallC3×C7×C17×C23 ⋊ C4
derived, HallC3×C7×C17 ⋊ C4×C23
HallC7×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ #595
HallC17×C23 ⋊ Dic21
HallC7×C23 ⋊ C3⋊#595
HallC7×C17 ⋊ Dic3×C23
HallC3×C23 ⋊ C7⋊#595
HallC3×C17 ⋊ C23×Dic7
HallC3×C7 ⋊ C23×#595
SylowC17 ⋊ C23×Dic21
SylowC7 ⋊ C23×C3⋊#595
SylowC3 ⋊ C23×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC23C3⋊(C7⋊#595)
commutator, hypocenterC3×C7×C17C4×C23
FrattiniC1G
Fitting, socleC3×C7×C17×C23C4
prime radicalC3×C7×C23×D17C2
cosocleC3×C7×D17C2×C23
LCSG ▷ C3×C7×C17
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8211

Conjugacy classes & character table

2484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 64);