C₁₃×D₇×C₂₉⋊C₇ #49149232

order	36946
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₇×C₂₉⋊C₇
unambiguous semidirect product	C₇⋊(C₂×C₁₃×C₂₉⋊C₇)
unambiguous semidirect product	(D₇×C₂₉)⋊(C₇×C₁₃)
unambiguous semidirect product	(C₁₃×D₇×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₁₃	D₇×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₇×C₂₉	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₂×C₇
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₁₃

44 conjugacy classes of subgroups.

μ_t(G) = 2639

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36946, 18);