C₂×C₇×C₃⋊D₃×C₉₇ #37568001

order	24444
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₉₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₇×C₃⋊D₃×C₉₇
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₇×C₉₇)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₉₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₇×C₉₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₉₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇×C₉₇

120 conjugacy classes of subgroups.

μ_t(G) = 12222

8148 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 264);