#44510083

order	30848
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³×C₄

Aliases

No aliases for this group.

Fitting	C₄×C₄⋊C₄×C₂₄₁ ⋊ C₂
Sylow	C₂₄₁ ⋊ #2319

540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.

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

μ_t(G) = 15424

Polycyclic presentation:

2^7,241|a^2=g,b^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^240

4844 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 7148);