C₉₇×C₁₀₉⋊C₃ #44540552

order	31719
automorphism	?
homology	Abelianization (H₁) = C₃×C₉₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉₇×C₁₀₉⋊C₃
unambiguous semidirect product	C₁₀₉⋊(C₃×C₉₇)

Fitting, socle, Hall	C₉₇×C₁₀₉ ⋊ C₃
derived, Sylow	C₁₀₉ ⋊ C₃×C₉₇

	subgroup	G/H
center, hypercenter	C₉₇	C₁₀₉⋊C₃
commutator, cosocle, hypocenter	C₁₀₉	C₃×C₉₇
Frattini	C₁	G
Fitting, socle	C₉₇×C₁₀₉	C₃
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₉₇

8 conjugacy classes of subgroups.

μ_t(G) = 10573

3783 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31719, 2);