C₁₇×C₃⋊D₃×C₇₉ #37563643

order	24174
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₇₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₇×C₃⋊D₃×C₇₉
unambiguous semidirect product	C₃⋊(D₃×C₁₇×C₇₉)

	subgroup	G/H
center, hypercenter	C₁₇×C₇₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₇₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇×C₇₉

48 conjugacy classes of subgroups.

μ_t(G) = 12087

8058 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24174, 29);