Finite Group Databasebeta

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ΓL(1,𝔽8)×C25×C59 #44526408

order30975
automorphism?
homologyAbelianization (H1) = C3×C25×C59 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C25×C59
unambiguous semidirect productC7⋊(C3×C25×C59)
unambiguous semidirect product(C7×C25)⋊(C3×C59)
unambiguous semidirect product(C7×C59)⋊(C3×C25)
unambiguous semidirect product(C7×C25×C59)⋊C3

Splittings

Fitting, HallC7×C25×C59 ⋊ C3
derived, SylowC7 ⋊ C3×C25×C59
HallC7×C59 ⋊ C3×C25
HallC7×C25 ⋊ C3×C59

Subgroups

subgroupG/H
center, hypercenterC25×C59ΓL(1,𝔽8)
commutator, hypocenterC7C3×C25×C59
FrattiniC5C5×ΓL(1,𝔽8)×C59
FittingC7×C25×C59C3
socleC5×C7×C59C3×C5
prime radicalC5×ΓL(1,𝔽8)×C59C5
cosocleC5×C7C3×C5×C59
LCSG ▷ C7
UCSC1 ◁ C25×C59

24 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, 2);