C₂²⋊(C₆₇₃⋊C₉) #37564498

order	24228
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₂²⋊(C₆₇₃⋊C₉)
unambiguous semidirect product	C₆₇₃⋊(C₂²⋊C₉)

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊(C₆₇₃⋊C₃)
commutator, hypocenter	C₂²×C₆₇₃	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₆₇₃	C₃
LCS	G ▷ C₂²×C₆₇₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

μ_t(G) = 12114

Polycyclic presentation:

3,2^2,673,3|a^3=e,b^a=c,c^a=bc,d^a=d^255

2700 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24228, 13);