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(C5×ΓL(1,𝔽32))⋊C25 #34084241

order19375
automorphism?
homologyAbelianization (H1) = C5×C25 · Schur multiplier (H2) = C52

Aliases

unambiguous semidirect product(C5×ΓL(1,𝔽32))⋊C25

Splittings

FittingC5×C25×C31 ⋊ C5
SylowC31 ⋊ C52⋊C25

Subgroups

subgroupG/H
center, FrattiniC52C5×ΓL(1,𝔽32)
commutatorC5×C31C5×C25
FittingC5×C25×C31C5
socle, cosocleC52×C31C52
prime radicalC52×ΓL(1,𝔽32)C5
hypercenterC5×C25ΓL(1,𝔽32)
hypocenterC31C52⋊C25
LCSG ▷ C5×C31 ▷ C31
UCSC1 ◁ C52 ◁ C5×C25

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3875

Polycyclic presentation:

5^4,31|a^5=d,b^a=bc,e^b=e^16

Conjugacy classes & character table

895 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19375, 18);