D₇² #5998

order	196
isoclinism	isoclinic class of D₇²
automorphism	Aut(G) = #72241578 (order 3528) · Inn(G) = G · Out(G) = C₃×D₃
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇²
unambiguous semidirect product	(C₇×D₇)⋊C₂
unambiguous semidirect product	(C₇⋊D₇)⋊C₂

C₇² ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²	C₂²
LCS	G ▷ C₇²
UCS	C₁

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 14

A minimal faithful permutation representation — 2 generators on 14 points:

(1,5,7,13,12,10,4,2,3,9,11,14,8,6);(1,5,8,13,11,10,3,2,4,9,12,14,7,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(196, 9);