Finite Group Databasebeta

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C3×C5×C23⋊#595 #37553292

order23460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C23⋊#595
unambiguous semidirect productC23⋊(C3×C5×#595)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C4
derived, HallC17×C23 ⋊ C3×C4×C5
HallC5×C17×C23 ⋊ C3×C4
HallC3×C17×C23 ⋊ C4×C5
HallC3×C5×C23 ⋊ #595
HallC3×C5×C17 ⋊ Dic23
HallC5×C23 ⋊ C3×#595
HallC5×C17 ⋊ C3×Dic23
HallC3×C23 ⋊ C5×#595
HallC3×C17 ⋊ C5×Dic23
SylowC23 ⋊ C3×C5×#595
SylowC17 ⋊ C3×C5×Dic23

Subgroups

subgroupG/H
center, hypercenterC3×C5C23⋊#595
commutator, hypocenterC17×C23C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C23C4
prime radicalC3×C5×C23×D17C2
cosocleC23×D17C2×C3×C5
LCSG ▷ C17×C23
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 19);