#36375194

order	22336
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₄₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13063703
commutator, socle, prime radical	C₂²×C₃₄₉	C₂²×C₄
Fitting	C₄⋊C₄×C₃₄₉	C₄
cosocle	C₂×Dic₃₄₉	C₂³
hypercenter	C₄⋊C₄	#13063703
hypocenter	C₃₄₉	#446
LCS	G ▷ C₂²×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 22336

Polycyclic presentation:

2^6,349|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^213,g^c=g^213,g^e=g^348

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22336, 1599);