#29833800

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Fitting	C₂³×D₈×C₆₁ ⋊ C₂
Sylow	C₆₁ ⋊ #33517

1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.

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

μ_t(G) = 1952

Polycyclic presentation:

2^8,61|e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,g^a=gh,i^a=i^60,e^b=eg,g^b=gh

1726 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323355);