#10604988⋊C₃ #14511604

order	1920
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, hypercenter	C₂	#65800⋊C₃
commutator, Fitting, hypocenter	C₂²×C₅×Q₈	C₃×C₄
Frattini	C₂³	A₄×AGL(1,𝔽₅)
socle	C₂³×C₅	C₄×A₄
prime radical	D₅×C₂²⋊SL(2,𝔽₃)	C₂
cosocle	C₂²×Q₈×D₅	C₂×C₃
LCS	G ▷ C₂²×C₅×Q₈
UCS	C₁ ◁ C₂

322 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

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

μ_t(G) = 120

Polycyclic presentation:

2,3,2^5,5,2|a^2=c,d^2=i,e^2=i,d^a=df,e^a=efg,h^a=h^2,d^b=de,e^b=d,f^b=g,g^b=fg,h^c=h^4,e^d=ei

maximal subgroup of	#72253825
maximal quotient of	#72253793

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237302);