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#49185661

order	38125
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

C₆₁ ⋊ C₁₂₅⋊C₅

Subgroups

	subgroup	G/H
center, Frattini	C₂₅	C₅×C₆₁⋊C₅
commutator, socle	C₅×C₆₁	C₅×C₂₅
Fitting	C₅×C₂₅×C₆₁	C₅
prime radical	C₅²×C₆₁	C₂₅
cosocle	C₂₅×C₆₁	C₅²
hypercenter	C₅×C₂₅	C₆₁⋊C₅
hypocenter	C₆₁	C₁₂₅⋊C₅
LCS	G ▷ C₅×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂₅ ◁ C₅×C₂₅

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7625

Polycyclic presentation:

5^4,61|a^5=c,c^5=d,b^a=bd,e^a=e^9

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38125, 31);