#41002970

order	26944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₄₂₁ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₂₁
commutator, socle, prime radical	C₂²×C₄₂₁	C₂²×C₄
Fitting	C₄×C₈×C₄₂₁	C₂
cosocle	C₂×C₄×C₄₂₁	C₂³
hypercenter	C₄×C₈	D₄₂₁
hypocenter	C₄₂₁	#446
LCS	G ▷ C₂²×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

94 conjugacy classes of subgroups.

μ_t(G) = 26944

Polycyclic presentation:

2^6,421|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^420

6748 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 679);