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C23×C3⋊#66776 #37553322

order23460
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊#66776
unambiguous semidirect productC3⋊(C23×#66776)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C23
HallC5×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ AGL(1,𝔽5)
HallC17×C23 ⋊ ΓL(1,𝔽16)
HallC3×C5×C23 ⋊ #595
HallC5×C23 ⋊ C3⋊#595
HallC5×C17 ⋊ Dic3×C23
HallC3×C23 ⋊ #66776
HallC3×C17 ⋊ AGL(1,𝔽5)×C23
SylowC17 ⋊ C23×ΓL(1,𝔽16)
HallC3×C5 ⋊ C23×#595
SylowC5 ⋊ C23×C3⋊#595
SylowC3 ⋊ C23×#66776

Subgroups

subgroupG/H
center, hypercenterC23C3⋊#66776
commutator, hypocenterC3×C5×C17C4×C23
FrattiniC1G
Fitting, socleC3×C5×C17×C23C4
prime radicalC3×C23×D85C2
cosocleC3×D85C2×C23
LCSG ▷ C3×C5×C17
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1587 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 49);