D₃×C₂₃×D₇₅ #35207966

order	20700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₂₃×D₇₅
unambiguous semidirect product	(C₃×D₃)⋊(C₂₃×D₂₅)
unambiguous semidirect product	(D₃×C₂₅)⋊(D₃×C₂₃)

	subgroup	G/H
center, hypercenter	C₂₃	D₃×D₇₅
commutator, cosocle, hypocenter	C₃²×C₂₅	C₂²×C₂₃
Frattini	C₅	D₃×C₂₃×D₁₅
Fitting	C₃²×C₂₃×C₂₅	C₂²
socle	C₃²×C₅×C₂₃	C₂×D₅
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₂₃

132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

μ_t(G) = 3450

2691 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 82);