C₉⋊#95 #63390

order	288
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

C₉ ⋊ #95

	subgroup	G/H
center	C₂³	C₂×D₉
commutator	C₂×C₉	C₄²
Frattini, socle, prime radical	C₂³×C₃	C₂×D₃
Fitting	C₂²×C₄×C₉	C₂
cosocle	C₂³×C₉	C₂²
hypercenter	C₂²×C₄	D₉
hypocenter	C₉	#95
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

114 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 2 generators on 21 points:

(1,6,8,7,2,4,3,9,5)(14,15,16,17)(19,21);(2,4)(3,7)(5,6)(8,9)(10,11,12,13)(18,19)(20,21)

Polycyclic presentation:

2^5,3^2|a^2=c,b^2=d,f^3=g^2,b^a=be,f^a=f^2g,g^a=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 38);