order	484
isoclinism	isoclinic class of C₁₁⋊D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product	C₂×C₁₁⋊D₁₁
unambiguous semidirect product	(C₂×C₁₁)⋊D₁₁

Splittings

Fitting, socle	C₂×C₁₁² ⋊ C₂
derived, Sylow	C₁₁² ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 242

A minimal faithful permutation representation — 3 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(484, 11);