#13088350

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃²⋊AGL(1,𝔽₅)
commutator	C₂×C₅×C₃⋊D₃	C₂×C₄
Fitting, socle	C₂×C₃²×C₅	C₂²⋊C₄
prime radical	#10624029	C₂
cosocle	C₂×D₅×C₃⋊D₃	C₂²
hypocenter	C₃²×C₅	#99
LCS	G ▷ C₂×C₅×C₃⋊D₃ ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 192 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) = 120

Polycyclic presentation:

2^5,3^2,5|a^2=c,b^a=bd,d^a=de,f^a=f^2,g^a=f^2g,h^a=h^2,c^b=ce,f^b=f^2g^2,h^c=h^4,f^d=f^2,g^d=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4667);