#11925016

order	1200
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Hall	C₅²⋊C₃ ⋊ C₂²⋊C₄
Sylow	C₅² ⋊ (C₂×D₃)⋊C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂²	#3874⋊C₂
commutator	C₂×C₅²⋊C₃	C₂×C₄
Fitting, socle	C₂²×C₅²	C₂×D₃
prime radical	C₂²×#3874	C₂
cosocle	C₂²×C₅²⋊C₃	C₂²
hypocenter	C₅²⋊C₃	C₂²⋊C₄
LCS	G ▷ C₂×C₅²⋊C₃ ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂²

102 conjugacy classes of subgroups.

μ_t(G) = 120

Polycyclic presentation:

2^4,3,5^2|b^2=c,b^a=bd,e^a=e^2,f^a=g,g^a=f,e^b=e^2,f^b=g^4,g^b=f^4,f^e=g,g^e=f^4g^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 226);