C₂²×C₁₃⋊C₃×C₄₉⋊C₃ #37524231

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₁₃⋊C₃×C₄₉⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	C₁₃⋊C₃×C₄₉⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂²×C₃²
Frattini	C₇	C₂²×ΓL(1,𝔽₈)×C₁₃⋊C₃
Fitting	C₂²×C₁₃×C₄₉	C₃²
socle	C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)
LCS	G ▷ C₁₃×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) = 2548

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 176);