#36355923

order	22144
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

No aliases for this group.

Fitting	C₄×C₄⋊C₄×C₁₇₃ ⋊ C₂
Sylow	C₁₇₃ ⋊ #2275

780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.

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

μ_t(G) = 11072

Polycyclic presentation:

2^7,173|a^2=f,b^2=g,c^2=f,b^a=be,d^a=de,c^b=ce,h^c=h^172,h^d=h^172

3508 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 6870);