D₇×C₃⋊(D₁₁⋊C₂₅) #37528234

order	23100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₃⋊(D₁₁⋊C₂₅)
unambiguous semidirect product	(C₃×D₇)⋊(D₁₁⋊C₂₅)
unambiguous semidirect product	(D₇×D₃₃)⋊C₂₅
unambiguous semidirect product	(D₇×C₁₁⋊C₂₅)⋊D₃

	subgroup	G/H
center, Frattini, hypercenter	C₅	D₇×C₃⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₃×C₇×C₁₁	C₂²×C₂₅
Fitting, socle, cosocle	C₃×C₅×C₇×C₁₁	C₂²×C₅
prime radical	C₅×D₇×D₃₃	C₅
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₅

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

μ_t(G) = 5775

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 45);