C₁₁²×D₉ #14546100

order	2178
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁² · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₁₁²×D₉
unambiguous semidirect product	C₉⋊(C₂×C₁₁²)

Fitting, Hall	C₉×C₁₁² ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₁²

	subgroup	G/H
center, hypercenter	C₁₁²	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₁²
Frattini	C₃	D₃×C₁₁²
Fitting	C₉×C₁₁²	C₂
socle	C₃×C₁₁²	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₁²

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1089

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11)(23,24,25,26,27,28,29,30,31);(12,13,14,15,16,17,18,19,20,21,22)(24,31)(25,30)(26,29)(27,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2178, 17);