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C2×C17×ΓL(1,𝔽8)×C47 #46776751

order33558
automorphism?
homologyAbelianization (H1) = C2×C3×C17×C47 · Schur multiplier (H2) = C1

Aliases

direct productC2×C17×ΓL(1,𝔽8)×C47
unambiguous semidirect product(C2×C7)⋊(C3×C17×C47)
unambiguous semidirect product(C2×C7×C17)⋊(C3×C47)
unambiguous semidirect product(C2×C7×C47)⋊(C3×C17)
unambiguous semidirect product(C2×C7×C17×C47)⋊C3

Splittings

Fitting, socle, HallC2×C7×C17×C47 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C17×C47
HallC7×C17×C47 ⋊ C2×C3
HallC2×C7×C47 ⋊ C3×C17
HallC7×C47 ⋊ C2×C3×C17
HallC2×C7×C17 ⋊ C3×C47
HallC7×C17 ⋊ C2×C3×C47
HallC2×C7 ⋊ C3×C17×C47

Subgroups

subgroupG/H
center, hypercenterC2×C17×C47ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C17×C47
FrattiniC1G
Fitting, socleC2×C7×C17×C47C3
LCSG ▷ C7
UCSC1 ◁ C2×C17×C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11186

Conjugacy classes & character table

7990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33558, 2);