C₂×C₇×C₁₃×C₂₉⋊C₇ #49149235

order	36946
automorphism	?
homology	Abelianization (H₁) = C₂×C₇²×C₁₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₂×C₇×C₁₃×C₂₉⋊C₇
unambiguous semidirect product	(C₂×C₂₉)⋊(C₇²×C₁₃)
unambiguous semidirect product	(C₂×C₇×C₂₉)⋊(C₇×C₁₃)
unambiguous semidirect product	(C₂×C₁₃×C₂₉)⋊C₇²
unambiguous semidirect product	(C₂×C₇×C₁₃×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₂×C₇²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₇×C₁₃

80 conjugacy classes of subgroups.

μ_t(G) = 5278

2002 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36946, 21);