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#28478486

order	15104
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄²

Aliases

No aliases for this group.

Splittings

C₅₉ ⋊ #7960

Subgroups

	subgroup	G/H
center	C₂²	C₂×C₅₉⋊#95
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×#423	C₂
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁴×C₅₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×#423	D₅₉
hypocenter	C₅₉	#7960
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#423

608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3776

Polycyclic presentation:

2^8,59|a^2=e,b^2=f,c^2=g,d^2=gh,f^2=g,b^a=bd,d^a=dg,f^a=fgh,i^a=i^58,c^b=cg,e^b=eh,i^b=i^58

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59365);