C₃⋊#10617016 #14513677

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

derived	C₃×2₋¹⁺⁴⋊C₅ ⋊ C₄
Sylow	C₃ ⋊ #10617016

	subgroup	G/H
center, Frattini, hypercenter	C₂²	C₃⋊((C₂⁴⋊C₅)⋊C₂)
commutator, hypocenter	C₃×2₋¹⁺⁴⋊C₅	C₄
Fitting	C₂×C₃×2₋¹⁺⁴	D₅
socle	C₂²×C₃	(C₂⁴⋊C₅)⋊C₂
prime radical, cosocle	C₂×C₃×2₋¹⁺⁴⋊C₅	C₂
LCS	G ▷ C₃×2₋¹⁺⁴⋊C₅
UCS	C₁ ◁ C₂²

262 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.

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

μ_t(G) = 384

Polycyclic presentation:

2^2,3,5,2^5|a^2=b,e^2=i,f^2=i,g^2=i,c^a=c^2,d^a=d^4,e^a=efghi,f^a=fh,g^a=ghi,e^d=f,f^d=fg,g^d=gh,h^d=ehi,f^e=fi,g^e=gi,h^e=hi,g^f=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 239375);