#29601077

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₆₁×Q₁₂₈ ⋊ C₂
Sylow	C₆₁ ⋊ #13743

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 7808

Polycyclic presentation:

2^8,61|b^2=h,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ch,d^a=de,e^a=ef,f^a=fg,g^a=gh,i^a=i^60,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^c=i^60

1096 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 90632);