C₂×D₁₁₂ #89674

order	448
isoclinism	isoclinic class of D₁₁₂
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₁₁₂

Fitting	C₂×C₇×C₁₆ ⋊ C₂
Sylow	C₇ ⋊ C₂×D₁₆

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 436);