Finite Group Databasebeta

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C3×C7×ΓL(1,𝔽8)×C59 #39907299

order26019
automorphism?
homologyAbelianization (H1) = C32×C7×C59 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×ΓL(1,𝔽8)×C59
unambiguous semidirect productC7⋊(C32×C7×C59)
unambiguous semidirect product(C3×C7)⋊(C3×C7×C59)
unambiguous semidirect product(C7×C59)⋊(C32×C7)
unambiguous semidirect product(C3×C7×C59)⋊(C3×C7)

Splittings

Fitting, socleC3×C72×C59 ⋊ C3
derivedC7 ⋊ C32×C7×C59
HallC72×C59 ⋊ C32
SylowC72 ⋊ C32×C59

Subgroups

subgroupG/H
center, hypercenterC3×C7×C59ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C7×C59
FrattiniC1G
Fitting, socleC3×C72×C59C3
LCSG ▷ C7
UCSC1 ◁ C3×C7×C59

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3717

Conjugacy classes & character table

6195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26019, 11);