C₂×#6435 #90163

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Fitting	C₂×C₄²×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂×#117

330 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 925);