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C17×C23×ΓL(1,𝔽16) #37553318

order23460
automorphism?
homologyAbelianization (H1) = C4×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC17×C23×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C17×AGL(1,𝔽5)×C23)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C4
derived, HallC3×C5 ⋊ C4×C17×C23
HallC5×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C23
HallC5×C23 ⋊ Dic3×C17
HallC5×C17 ⋊ Dic3×C23
HallC3×C23 ⋊ C17×AGL(1,𝔽5)
HallC3×C17 ⋊ AGL(1,𝔽5)×C23
SylowC5 ⋊ Dic3×C17×C23
SylowC3 ⋊ C17×AGL(1,𝔽5)×C23

Subgroups

subgroupG/H
center, hypercenterC17×C23ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C17×C23
FrattiniC1G
Fitting, socleC3×C5×C17×C23C4
prime radicalC3×D5×C17×C23C2
cosocleC3×D5C2×C17×C23
LCSG ▷ C3×C5
UCSC1 ◁ C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

3519 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 45);