Q₈×Dic₉ #63507

order	288
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₉ ⋊ C₄×Q₈

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

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 155);