C₇₁⋊#7317 #31884753

order	18176
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

C₇₁ ⋊ #7317

432 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

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

μ_t(G) = 2272

Polycyclic presentation:

2^8,71|a^2=d,b^2=e,d^2=h,e^2=h,b^a=bc,c^a=cf,e^a=eg,g^a=gh,c^b=cg,d^b=df,f^b=fh,i^b=i^70,e^d=eh

1148 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 56869);