C₇×D₇×D₁₇₁ #45691671

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₇×D₁₇₁
unambiguous semidirect product	(C₉×D₇)⋊(C₇×D₁₉)
unambiguous semidirect product	(D₇×C₁₉)⋊(C₇×D₉)

	subgroup	G/H
center, hypercenter	C₇	D₇×D₁₇₁
commutator, cosocle, hypocenter	C₇×C₉×C₁₉	C₂²×C₇
Frattini	C₃	C₇×D₇×D₅₇
Fitting	C₇²×C₉×C₁₉	C₂²
socle	C₃×C₇²×C₁₉	C₂×D₃
LCS	G ▷ C₇×C₉×C₁₉
UCS	C₁ ◁ C₇

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

normal subgroups only

This group has 156 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) = 2394

3045 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 469);