C₂²×C₂²⋊C₂₇ #88578

order	432
isoclinism	isoclinic class of A₄
automorphism	Aut(G) = D₃×C₉×S₄ (order 1296) · Inn(G) = A₄ · Out(G) = C₂×D₃×C₉
homology	Abelianization (H₁) = C₂²×C₂₇ · Schur multiplier (H₂) = C₂²

Aliases

C₂²×C₂²⋊C₂₇

derived	C₂² ⋊ C₂²×C₂₇
Sylow	C₂⁴ ⋊ C₂₇

97 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 35 points:

(3,4)(6,7,8)(9,14,26,17,29,28,31,10,19,12,22,32,25,34,13,16,15,27,18,30,35,11,21,20,24,23,33);(1,2)(5,8)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 225);