#46831225

order	34624
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₅₄₁ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#14524194
commutator, socle, prime radical	C₂²×C₅₄₁	C₂²×C₄
Fitting	C₄⋊C₄×C₅₄₁	C₄
cosocle	C₂×Dic₅₄₁	C₂³
hypercenter	C₄⋊C₄	#14524194
hypocenter	C₅₄₁	#446
LCS	G ▷ C₂²×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 34624

Polycyclic presentation:

2^6,541|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^52,g^c=g^52,g^e=g^540

1378 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34624, 1599);