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C3×C7×C17×C22⋊ΓL(1,𝔽8) #44473003

order29988
automorphism?
homologyAbelianization (H1) = C32×C7×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×C17×C22⋊ΓL(1,𝔽8)
unambiguous semidirect product(C22×C3)⋊(C7×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7)⋊(C7×A4×C17)
unambiguous semidirect product(C22×C3×C17)⋊(C7×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7×C17)⋊(C7×A4)

Splittings

Fitting, socleC22×C3×C72×C17 ⋊ C3
derivedC22×C7 ⋊ C32×C7×C17
HallC22×C72×C17 ⋊ C32
HallC72×C17 ⋊ C3×A4
HallC22×C72 ⋊ C32×C17
HallC22×C17 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×A4×C17
SylowC22 ⋊ C3×C7×C17×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C7×C17C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C7×C17
FrattiniC1G
Fitting, socleC22×C3×C72×C17C3
LCSG ▷ C22×C7
UCSC1 ◁ C3×C7×C17

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2142

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 644);