C₇×C₁₉⋊C₃×C₇₉ #44538584

order	31521
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉⋊C₃×C₇₉
unambiguous semidirect product	C₁₉⋊(C₃×C₇×C₇₉)

	subgroup	G/H
center, hypercenter	C₇×C₇₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₇₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₇₉

16 conjugacy classes of subgroups.

μ_t(G) = 10507

4977 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31521, 3);