#36378837

order	22592
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₅₃ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13083443
commutator, socle, prime radical	C₂²×C₃₅₃	C₂²×C₄
Fitting	C₄⋊C₄×C₃₅₃	C₄
cosocle	C₂×Dic₃₅₃	C₂³
hypercenter	C₄⋊C₄	#13083443
hypocenter	C₃₅₃	#446
LCS	G ▷ C₂²×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 22592

Polycyclic presentation:

2^6,353|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^311,g^c=g^311,g^e=g^352

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22592, 1599);