#35217111

order	20864
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

No aliases for this group.

Fitting	C₂²×C₂²⋊C₄×C₁₆₃ ⋊ C₂
Sylow	C₁₆₃ ⋊ #2308

1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.

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

μ_t(G) = 5216

Polycyclic presentation:

2^7,163|a^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^162

3284 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 7085);