#29508768

order	15424
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₄₁ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11757210
commutator, socle, prime radical	C₂²×C₂₄₁	C₂²×C₄
Fitting	C₂×Q₈×C₂₄₁	C₄
cosocle	C₂×Dic₂₄₁	C₂³
hypercenter	C₂×Q₈	#11757210
hypocenter	C₂₄₁	#446
LCS	G ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

94 conjugacy classes of subgroups.

μ_t(G) = 15424

Polycyclic presentation:

2^6,241|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^64,g^c=g^177,g^e=g^240

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 1600);