D₅₅⋊D₁₁₇ #38787917

order	25740
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₅₅⋊D₁₁₇

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₁×C₁₃	C₂²
Frattini	C₃	D₅₅⋊D₃₉
socle	C₃×C₅×C₁₁×C₁₃	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₁×C₁₃
UCS	C₁

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

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

μ_t(G) = 6435

Polycyclic presentation:

2^2,3,5,11,13,3|c^3=g^2,c^a=c^2g,e^a=e^10,f^a=f^12,g^a=g^2,d^b=d^4,e^b=e^10

1710 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 148);