C₂²⋊(C₈₂₃⋊C₉) #44444201

order	29628
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₂²⋊(C₈₂₃⋊C₉)
unambiguous semidirect product	C₈₂₃⋊(C₂²⋊C₉)

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊(C₈₂₃⋊C₃)
commutator, hypocenter	C₂²×C₈₂₃	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₈₂₃	C₃
LCS	G ▷ C₂²×C₈₂₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

μ_t(G) = 14814

Polycyclic presentation:

3,2^2,823,3|a^3=e,b^a=c,c^a=bc,d^a=d^174

3300 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29628, 10);