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C4×C17×#63270 #32915409

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×#63270

Splittings

Fitting, HallC4×C7×C13×C17 ⋊ C3
derived, HallC7×C13 ⋊ C3×C4×C17
HallC7×C13×C17 ⋊ C3×C4
HallC4×C13×C17 ⋊ ΓL(1,𝔽8)
HallC4×C7×C17 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C3×C17
HallC13×C17 ⋊ C4×ΓL(1,𝔽8)
HallC7×C17 ⋊ C4×C13⋊C3
HallC4×C13 ⋊ C17×ΓL(1,𝔽8)
HallC4×C7 ⋊ C17×C13⋊C3
SylowC13 ⋊ C4×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C17#63270
commutator, hypocenterC7×C13C3×C4×C17
FrattiniC2C2×C17×#63270
FittingC4×C7×C13×C17C3
socleC2×C7×C13×C17C2×C3
prime radicalC2×C17×#63270C2
cosocleC2×C7×C13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C4×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6188

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 4);