#46838202

order	34688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₄×C₁₆×C₂₇₁ ⋊ C₂
Sylow	C₂₇₁ ⋊ #2170

146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

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

μ_t(G) = 8672

Polycyclic presentation:

2^7,271|a^2=e,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^270,d^b=dg,h^b=h^270

8696 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 6348);