#44536854

order	31424
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₄₉₁ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₉₁
commutator, socle, prime radical	C₂²×C₄₉₁	C₂²×C₄
Fitting	C₄⋊C₈×C₄₉₁	C₂
cosocle	C₂×C₄×C₄₉₁	C₂³
hypercenter	C₄⋊C₈	D₄₉₁
hypocenter	C₄₉₁	#446
LCS	G ▷ C₂²×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

94 conjugacy classes of subgroups.

μ_t(G) = 31424

Polycyclic presentation:

2^6,491|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^490,g^c=g^490

4928 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 678);