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#34084264

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

Aliases

No aliases for this group.

Splittings

SylowC31 ⋊ #10597833

Subgroups

subgroupG/H
centerC5C52⋊ΓL(1,𝔽32)
commutator, cosocleC52×C31C52
FrattiniC52C5×ΓL(1,𝔽32)
Fitting, prime radicalC31×H(3,𝔽5)C5
socleC5×C31H(3,𝔽5)
hypercenterH(3,𝔽5)ΓL(1,𝔽32)
hypocenterC31#10597833
LCSG ▷ C52×C31 ▷ C5×C31 ▷ C31
UCSC1 ◁ C5 ◁ C52 ◁ H(3,𝔽5)

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3875

Polycyclic presentation:

5^4,31|b^5=d^2,b^a=bc,c^a=cd,e^b=e^16

Conjugacy classes & character table

223 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19375, 41);