#27135116

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Fitting	C₂×C₄⋊C₄×C₁₉₃ ⋊ C₂
Sylow	C₁₉₃ ⋊ #380

234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

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

Polycyclic presentation:

2^6,193|a^2=f,b^2=d,b^a=bd,c^a=ce,g^c=g^192

1948 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 406);