#34069229

order	19328
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₅₁ ⋊ #1832

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₅₁
commutator, socle, prime radical	C₂³×C₁₅₁	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₁₅₁	C₂
cosocle	C₂²×C₄×C₁₅₁	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₅₁
hypocenter	C₁₅₁	#1832
LCS	G ▷ C₂³×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

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

μ_t(G) = 19328

Polycyclic presentation:

2^7,151|a^2=f,b^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^150,h^c=h^150

3044 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4629);