C₃₇×C₁₉₉⋊C₃ #36348288

order	22089
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₇×C₁₉₉⋊C₃
unambiguous semidirect product	C₁₉₉⋊(C₃×C₃₇)

Fitting, socle, Hall	C₃₇×C₁₉₉ ⋊ C₃
derived, Sylow	C₁₉₉ ⋊ C₃×C₃₇

	subgroup	G/H
center, hypercenter	C₃₇	C₁₉₉⋊C₃
commutator, cosocle, hypocenter	C₁₉₉	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃₇×C₁₉₉	C₃
LCS	G ▷ C₁₉₉
UCS	C₁ ◁ C₃₇

8 conjugacy classes of subgroups.

μ_t(G) = 7363

2553 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22089, 2);