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#38785291

order25625
automorphism?
homologyAbelianization (H1) = C52 · Schur multiplier (H2) = C5

Aliases

No aliases for this group.

Splittings

FittingC41×5−1+2 ⋊ C5
SylowC41 ⋊ #10597831

Subgroups

subgroupG/H
centerC5C52⋊(C41⋊C5)
commutator, cosocleC52×C41C52
FrattiniC52C5×C41⋊C5
FittingC41×5−1+2C5
socleC5×C41H(3,𝔽5)
prime radicalC52×C41⋊C5C5
hypercenter5−1+2C41⋊C5
hypocenterC41#10597831
LCSG ▷ C52×C41 ▷ C5×C41 ▷ C41
UCSC1 ◁ C5 ◁ C52 ◁ 5−1+2

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1025

Polycyclic presentation:

5^4,41|a^5=d,b^a=bc,c^a=cd,e^b=e^10

Conjugacy classes & character table

281 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25625, 34);