#28407801

order	14464
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₁₃ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11744762
commutator, socle, prime radical	C₂²×C₁₁₃	C₂²×C₈
Fitting	C₄⋊C₄×C₁₁₃	C₈
cosocle	C₂×#11744753	C₂³
hypercenter	C₄⋊C₄	#11744762
hypocenter	C₁₁₃	#2183
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

126 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^95,h^b=h^112,h^c=h^18,h^e=h^98,h^f=h^112

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21737);