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C5×C17×#63270 #37550941

order23205
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×#63270

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C3
derived, HallC7×C13 ⋊ C3×C5×C17
HallC7×C13×C17 ⋊ C3×C5
HallC5×C13×C17 ⋊ ΓL(1,𝔽8)
HallC5×C7×C17 ⋊ C13⋊C3
HallC5×C7×C13 ⋊ C3×C17
HallC13×C17 ⋊ C5×ΓL(1,𝔽8)
HallC7×C17 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C17×ΓL(1,𝔽8)
HallC5×C7 ⋊ C17×C13⋊C3
SylowC13 ⋊ C5×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C17#63270
commutator, cosocle, hypocenterC7×C13C3×C5×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23205, 4);