C₄×Dic₁₈ #63430

order	288
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₁₈

C₉ ⋊ C₄×Q₈

	subgroup	G/H
center	C₂×C₄	C₂×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini, socle, prime radical	C₂²×C₃	C₂²×D₃
Fitting	C₄²×C₉	C₂
cosocle	C₂²×C₉	C₂³
hypercenter	C₄²	D₉
hypocenter	C₉	C₄×Q₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

105 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 78);