C₇×C₁₅₄₉⋊C₃ #45654286

order	32529
automorphism	?
homology	Abelianization (H₁) = C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₅₄₉⋊C₃
unambiguous semidirect product	C₁₅₄₉⋊(C₃×C₇)

Fitting, socle, Hall	C₇×C₁₅₄₉ ⋊ C₃
derived, Sylow	C₁₅₄₉ ⋊ C₃×C₇

	subgroup	G/H
center, hypercenter	C₇	C₁₅₄₉⋊C₃
commutator, cosocle, hypocenter	C₁₅₄₉	C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₅₄₉	C₃
LCS	G ▷ C₁₅₄₉
UCS	C₁ ◁ C₇

8 conjugacy classes of subgroups.

μ_t(G) = 10843

3633 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32529, 2);