C₂⁴×C₂²⋊#6923 #30626719

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁶

Aliases

direct product	C₂⁴×C₂²⋊#6923
unambiguous semidirect product	D₆₁⋊(C₂³×C₂²⋊C₄)
unambiguous semidirect product	(C₂×#6923)⋊C₂⁵

Fitting	C₂⁶×C₆₁ ⋊ C₄
Sylow	C₆₁ ⋊ C₂⁴×C₂²⋊C₄

43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 8408 normal subgroups are shown.

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

μ_t(G) = 3904

1120 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116274);