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C2×C13×ΓL(1,𝔽8)×C59 #44567249

order32214
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C59 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13×ΓL(1,𝔽8)×C59
unambiguous semidirect product(C2×C7)⋊(C3×C13×C59)
unambiguous semidirect product(C2×C7×C59)⋊(C3×C13)

Splittings

Fitting, socle, HallC2×C7×C13×C59 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C13×C59
HallC7×C13×C59 ⋊ C2×C3
HallC2×C7×C59 ⋊ C3×C13
HallC7×C59 ⋊ C2×C3×C13
HallC2×C7×C13 ⋊ C3×C59
HallC7×C13 ⋊ C2×C3×C59
HallC2×C7 ⋊ C3×C13×C59

Subgroups

subgroupG/H
center, hypercenterC2×C13×C59ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C13×C59
FrattiniC1G
Fitting, socleC2×C7×C13×C59C3
LCSG ▷ C7
UCSC1 ◁ C2×C13×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10738

Conjugacy classes & character table

7670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 3);