C₂²×Q₈×#10621924 #36370538

order	22144
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product	C₂²×Q₈×#10621924
unambiguous semidirect product	D₁₇₃⋊(C₂×C₄×Q₈)

Fitting	C₂²×Q₈×C₁₇₃ ⋊ C₄
Sylow	C₁₇₃ ⋊ C₂²×C₄×Q₈

1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.

normal subgroups only

This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.

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

μ_t(G) = 5536

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 21485);