#34323898

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Splittings

Fitting	C₇₉×#1788 ⋊ C₂
Sylow	C₇₉ ⋊ #24259

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1788	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂×#19099201	C₂
hypercenter	#1788	D₇₉
hypocenter	C₇₉	#24259
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1788

1566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5056

Polycyclic presentation:

2^8,79|b^2=eh,c^2=h,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^78,c^b=cg,f^b=fh,g^b=gh,i^b=i^78,d^c=dh,f^c=fh,g^c=gh,i^c=i^78,i^d=i^78

Conjugacy classes & character table

1528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 205197);