#46839275

order	34688
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Fitting	C₄×C₄⋊C₄×C₂₇₁ ⋊ C₂
Sylow	C₂₇₁ ⋊ #2349

704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.

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

μ_t(G) = 17344

Polycyclic presentation:

2^7,271|a^2=g,c^2=ef,b^a=be,c^a=cf,h^a=h^270,d^b=de,h^b=h^270,h^d=h^270

5450 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 7421);