#29502829⋊C₂ #44475584

order	30276
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	#29502829⋊C₂
unambiguous semidirect product	((C₂₉⋊D₂₉)⋊C₉)⋊C₂

derived, Hall	C₂₉²⋊C₉ ⋊ C₂²
Sylow	C₂₉² ⋊ C₂×D₉

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₉²⋊C₉	C₂²
Frattini	C₃	#19097943⋊C₂
Fitting, socle	C₃×C₂₉²	C₂×D₃
LCS	G ▷ C₂₉²⋊C₉
UCS	C₁

66 conjugacy classes of subgroups.

μ_t(G) = 261

Polycyclic presentation:

2^2,3,29^2,3|c^3=f^2,c^a=c^2f,d^a=d^20e^15,e^a=d^14e^9,f^a=f^2,c^b=c^2f,d^b=d^9e^14,e^b=d^15e^20,f^b=f^2,d^c=d^8e^14,e^c=de^20

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30276, 47);