#28390692

order	14464
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₁₃ ⋊ #1832

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₁₃
commutator, socle, prime radical	C₂³×C₁₁₃	C₂²×C₄
Fitting	#336×C₁₁₃	C₂
cosocle	C₂²×C₄×C₁₁₃	C₂³
hypercenter	#336	D₁₁₃
hypocenter	C₁₁₃	#1832
LCS	G ▷ C₂³×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

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

μ_t(G) = 14464

Polycyclic presentation:

2^7,113|a^2=f,b^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^112

2284 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 4628);