#34296606

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1939	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1939	D₇₉
hypocenter	C₇₉	#21675
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

674 conjugacy classes of subgroups.

μ_t(G) = 20224

Polycyclic presentation:

2^8,79|a^2=g,b^2=f,c^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,i^a=i^78,d^b=dh,i^b=i^78,d^c=dh,i^c=i^78,i^d=i^78

2260 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 177905);