C₅²×D₁₁×AGL(1,𝔽₇) #37528515

order	23100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×D₁₁×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₅²×D₁₁)

	subgroup	G/H
center, hypercenter	C₅²	D₁₁×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₁	C₂²×C₃
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₅²

320 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

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

μ_t(G) = 1925

1225 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 326);