C₇⋊(C₉⋊(C₂₃⋊AGL(1,𝔽₅))) #44394395

order	28980
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₇⋊(C₉⋊(C₂₃⋊AGL(1,𝔽₅)))
unambiguous semidirect product	C₉⋊(C₇⋊(C₂₃⋊AGL(1,𝔽₅)))
unambiguous semidirect product	C₂₃⋊(C₇⋊(C₉⋊AGL(1,𝔽₅)))

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₇×C₉×C₂₃	C₄
Frattini	C₃	C₃⋊(C₇⋊(C₂₃⋊AGL(1,𝔽₅)))
socle	C₃×C₅×C₇×C₂₃	Dic₃
prime radical	C₃×C₇×D₅×C₂₃	D₃
cosocle	C₇×C₉×D₅×C₂₃	C₂
LCS	G ▷ C₅×C₇×C₉×C₂₃
UCS	C₁

72 conjugacy classes of subgroups.

μ_t(G) = 7245

Polycyclic presentation:

2^2,3,5,7,23,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^6,f^a=f^22,g^a=g^2,d^b=d^4

2901 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 64);