C₇×D₉₉⋊D₁₃ #49114472

order	36036
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₉₉⋊D₁₃
unambiguous semidirect product	D₉₉⋊(C₇×D₁₃)
unambiguous semidirect product	D₁₁₇⋊(C₇×D₁₁)
unambiguous semidirect product	D₁₄₃⋊(C₇×D₉)

	subgroup	G/H
center, hypercenter	C₇	D₉₉⋊D₁₃
commutator, cosocle, hypocenter	C₉×C₁₁×C₁₃	C₂²×C₇
Frattini	C₃	C₇×D₃₃⋊D₁₃
Fitting	C₇×C₉×C₁₁×C₁₃	C₂²
socle	C₃×C₇×C₁₁×C₁₃	C₂×D₃
LCS	G ▷ C₉×C₁₁×C₁₃
UCS	C₁ ◁ C₇

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 9009

2436 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 140);