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C3×C17×ΓL(1,𝔽8)×C23 #37590149

order24633
automorphism?
homologyAbelianization (H1) = C32×C17×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×ΓL(1,𝔽8)×C23
unambiguous semidirect productC7⋊(C32×C17×C23)
unambiguous semidirect product(C3×C7)⋊(C3×C17×C23)
unambiguous semidirect product(C7×C17)⋊(C32×C23)
unambiguous semidirect product(C7×C23)⋊(C32×C17)
unambiguous semidirect product(C3×C7×C17)⋊(C3×C23)
unambiguous semidirect product(C3×C7×C23)⋊(C3×C17)
unambiguous semidirect product(C7×C17×C23)⋊C32
unambiguous semidirect product(C3×C7×C17×C23)⋊C3

Splittings

Fitting, socleC3×C7×C17×C23 ⋊ C3
derived, SylowC7 ⋊ C32×C17×C23
HallC7×C17×C23 ⋊ C32
HallC7×C23 ⋊ C32×C17
HallC7×C17 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC3×C17×C23ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C17×C23
FrattiniC1G
Fitting, socleC3×C7×C17×C23C3
LCSG ▷ C7
UCSC1 ◁ C3×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8211

Conjugacy classes & character table

5865 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24633, 4);