C₂²×D₂₈ #6544

order	224
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) order 129024
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₂₈

Fitting	C₂²×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 4 generators on 15 points:

(5,6,7,8)(9,10,12,14,15,13,11);(1,2)(3,4)(6,8)(10,11)(12,13)(14,15);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 176);