C₂₃⋊#11744621 #35207976

order	20700
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₃×C₂₅	C₄
Frattini	C₅	C₂₃⋊#4380
socle	C₃²×C₅×C₂₃	AGL(1,𝔽₅)
prime radical, cosocle	C₂₃×C₃⋊D₇₅	C₂
LCS	G ▷ C₃²×C₂₃×C₂₅
UCS	C₁

60 conjugacy classes of subgroups.

μ_t(G) = 3450

Polycyclic presentation:

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

1314 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 92);