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H(3,𝔽5)⋊(C61⋊C5) #49185662

order38125
automorphism?
homologyAbelianization (H1) = C52 · Schur multiplier (H2) = C52

Aliases

unambiguous semidirect productH(3,𝔽5)⋊(C61⋊C5)

Splittings

FittingC61×H(3,𝔽5) ⋊ C5
SylowC61 ⋊ H(3,𝔽5)⋊C5

Subgroups

subgroupG/H
centerC5C52⋊(C61⋊C5)
commutator, cosocleC52×C61C52
FrattiniC52C5×C61⋊C5
FittingC61×H(3,𝔽5)C5
socleC5×C61H(3,𝔽5)
hypercenterH(3,𝔽5)C61⋊C5
hypocenterC61H(3,𝔽5)⋊C5
LCSG ▷ C52×C61 ▷ C5×C61 ▷ C61
UCSC1 ◁ C5 ◁ C52 ◁ H(3,𝔽5)

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1525

Polycyclic presentation:

5^4,61|b^a=bc,c^a=cd,e^b=e^9

Conjugacy classes & character table

397 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38125, 32);