#14269201

order	1824
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₉
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	#125
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

112 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

μ_t(G) = 1824

Polycyclic presentation:

2^5,3,19|a^2=e,b^2=d,c^2=d,c^a=ce,g^a=g^18,c^b=cde,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 428);