Finite Group Databasebeta

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C3×C23×C7⋊#595 #45659283

order32844
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×C7⋊#595

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C23C7⋊#595
commutator, hypocenterC7×C17C3×C4×C23
FrattiniC1G
Fitting, socleC3×C7×C17×C23C4
prime radicalC3×C7×C23×D17C2
cosocleC7×D17C2×C3×C23
LCSG ▷ C7×C17
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8211

Conjugacy classes & character table

2622 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 48);