#13085461

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×ΓL(1,𝔽₁₆)
commutator, socle	C₂×C₃²×C₅	C₂×C₈
Fitting	C₃²×C₄×C₅	C₂×C₄
prime radical	C₂×C₃×D₁₅	C₈
cosocle	C₃²×#168	C₂²
hypocenter	C₃²×C₅	M₃₂
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₄

114 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 480

Polycyclic presentation:

2^5,3^2,5|a^2=c,b^2=d,c^2=d,d^2=e,b^a=be,f^a=f^2,h^a=h^2,g^b=g^2,h^c=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1778);