C₇×D₁₅×C₁₀₉ #37504332

order	22890
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₀₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₅×C₁₀₉
unambiguous semidirect product	C₃⋊(C₇×D₅×C₁₀₉)
unambiguous semidirect product	C₅⋊(D₃×C₇×C₁₀₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₀₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₇×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₀₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₀₉

32 conjugacy classes of subgroups.

μ_t(G) = 11445

6867 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22890, 17);