C₂²×C₁₉⋊C₃×C₄₉⋊C₃ #45691375

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₁₉⋊C₃×C₄₉⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	C₁₉⋊C₃×C₄₉⋊C₃
commutator, cosocle, hypocenter	C₁₉×C₄₉	C₂²×C₃²
Frattini	C₇	C₂²×ΓL(1,𝔽₈)×C₁₉⋊C₃
Fitting	C₂²×C₁₉×C₄₉	C₃²
socle	C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)
LCS	G ▷ C₁₉×C₄₉
UCS	C₁ ◁ C₂²

180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 3724

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 173);