#11925397

order	1200
isoclinism	isoclinic class of #10597189
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	#10597189
commutator	C₃×C₅⋊D₅	C₂×C₄
Fitting, socle	C₂×C₃×C₅²	D₄
prime radical	C₂×D₁₅⋊D₅	C₂
cosocle	C₂×C₃×C₅⋊D₅	C₂²
hypocenter	C₃×C₅²	C₂²⋊C₄
LCS	G ▷ C₃×C₅⋊D₅ ▷ C₃×C₅²
UCS	C₁ ◁ C₂

132 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 60

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 607);