C₇×D₉×C₁₉₉ #38736927

order	25074
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₁₉₉
unambiguous semidirect product	C₉⋊(C₂×C₇×C₁₉₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₇×C₁₉₉
Frattini	C₃	D₃×C₇×C₁₉₉
Fitting	C₇×C₉×C₁₉₉	C₂
socle	C₃×C₇×C₁₉₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₁₉₉

24 conjugacy classes of subgroups.

μ_t(G) = 12537

8358 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25074, 9);