C₂×C₂²⋊Q₈×#6157 #28328665

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product	C₂×C₂²⋊Q₈×#6157
unambiguous semidirect product	D₅₃⋊(C₄×C₂²⋊Q₈)

Fitting	C₂×C₂²⋊Q₈×C₅₃ ⋊ C₄
Sylow	C₅₃ ⋊ C₂×C₄×C₂²⋊Q₈

3854 conjugacy classes of subgroups.

μ_t(G) = 1696

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1114141);