Finite Group Databasebeta

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C5×C3⋊(C23⋊#595) #37553312

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

Aliases

direct productC5×C3⋊(C23⋊#595)
unambiguous semidirect productC3⋊(C5×C23⋊#595)
unambiguous semidirect productC23⋊(C5×C3⋊#595)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C4
derived, HallC3×C17×C23 ⋊ C4×C5
HallC5×C17×C23 ⋊ Dic3
HallC17×C23 ⋊ C5×Dic3
HallC3×C5×C23 ⋊ #595
HallC3×C5×C17 ⋊ Dic23
HallC5×C23 ⋊ C3⋊#595
HallC5×C17 ⋊ Dic69
HallC3×C23 ⋊ C5×#595
HallC3×C17 ⋊ C5×Dic23
SylowC23 ⋊ C5×C3⋊#595
SylowC17 ⋊ C5×Dic69
HallC3×C5 ⋊ C23⋊#595
SylowC3 ⋊ C5×C23⋊#595

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C23⋊#595)
commutator, hypocenterC3×C17×C23C4×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C23C4
prime radicalC3×C5×C23×D17C2
cosocleC3×C23×D17C2×C5
LCSG ▷ C3×C17×C23
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 39);