Finite Group Databasebeta

← Prev (#37590520) Next (#37590522) →

ΓL(1,𝔽8)×C25×C47 #37590521

order24675
automorphism?
homologyAbelianization (H1) = C3×C25×C47 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C25×C47
unambiguous semidirect productC7⋊(C3×C25×C47)
unambiguous semidirect product(C7×C25)⋊(C3×C47)
unambiguous semidirect product(C7×C47)⋊(C3×C25)
unambiguous semidirect product(C7×C25×C47)⋊C3

Splittings

Fitting, HallC7×C25×C47 ⋊ C3
derived, SylowC7 ⋊ C3×C25×C47
HallC7×C47 ⋊ C3×C25
HallC7×C25 ⋊ C3×C47

Subgroups

subgroupG/H
center, hypercenterC25×C47ΓL(1,𝔽8)
commutator, hypocenterC7C3×C25×C47
FrattiniC5C5×ΓL(1,𝔽8)×C47
FittingC7×C25×C47C3
socleC5×C7×C47C3×C5
prime radicalC5×ΓL(1,𝔽8)×C47C5
cosocleC5×C7C3×C5×C47
LCSG ▷ C7
UCSC1 ◁ C25×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8225

Conjugacy classes & character table

5875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24675, 2);