Finite Group Databasebeta

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C3×C19×ΓL(1,𝔽8)×C25 #44471683

order29925
automorphism?
homologyAbelianization (H1) = C32×C19×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×C19×ΓL(1,𝔽8)×C25
unambiguous semidirect productC7⋊(C32×C19×C25)
unambiguous semidirect product(C3×C7)⋊(C3×C19×C25)
unambiguous semidirect product(C7×C25)⋊(C32×C19)
unambiguous semidirect product(C3×C7×C25)⋊(C3×C19)

Splittings

FittingC3×C7×C19×C25 ⋊ C3
derived, SylowC7 ⋊ C32×C19×C25
HallC7×C19×C25 ⋊ C32
HallC7×C25 ⋊ C32×C19
HallC7×C19 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC3×C19×C25ΓL(1,𝔽8)
commutator, hypocenterC7C32×C19×C25
FrattiniC5C3×C5×C19×ΓL(1,𝔽8)
FittingC3×C7×C19×C25C3
socleC3×C5×C7×C19C3×C5
prime radicalC3×C5×C19×ΓL(1,𝔽8)C5
cosocleC5×C7C32×C5×C19
LCSG ▷ C7
UCSC1 ◁ C3×C19×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9975

Conjugacy classes & character table

7125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29925, 13);