C₃×D₄² #5875

order	192
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) = C₂×#72215688 (order 4096) · Inn(G) = C₂⁴ · Out(G) = C₂×#2196
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₃×D₄²

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

428 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 11 points:

(1,2,3)(4,5,6,7);(5,7);(8,9,10,11);(9,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1434);