Finite Group Databasebeta

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C52×ΓL(1,𝔽8)×C59 #44526412

order30975
automorphism?
homologyAbelianization (H1) = C3×C52×C59 · Schur multiplier (H2) = C5

Aliases

direct productC52×ΓL(1,𝔽8)×C59
unambiguous semidirect productC7⋊(C3×C52×C59)
unambiguous semidirect product(C5×C7)⋊(C3×C5×C59)
unambiguous semidirect product(C7×C59)⋊(C3×C52)
unambiguous semidirect product(C5×C7×C59)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C7×C59 ⋊ C3
derived, SylowC7 ⋊ C3×C52×C59
HallC7×C59 ⋊ C3×C52
HallC52×C7 ⋊ C3×C59

Subgroups

subgroupG/H
center, hypercenterC52×C59ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C52×C59
FrattiniC1G
Fitting, socleC52×C7×C59C3
LCSG ▷ C7
UCSC1 ◁ C52×C59

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10325

Conjugacy classes & character table

7375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30975, 6);