#34319259

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

Aliases

No aliases for this group.

	subgroup	G/H
center	C₄	C₇₉⋊#401
commutator, prime radical, cosocle	C₂⁴×C₇₉	C₂⁴
Frattini	C₂⁴	C₂³×D₇₉
Fitting	C₇₉×#1740	C₂
socle	C₂×C₇₉	C₂×#401
hypercenter	#1740	D₇₉
hypocenter	C₇₉	#23847
LCS	G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1740

604 conjugacy classes of subgroups.

μ_t(G) = 2528

Polycyclic presentation:

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

1762 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 200558);