C₂₅×SL(2,ℤ/4) #11924888

order	1200
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₅×SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊(C₄×C₂₅)

A₄ ⋊ C₄×C₂₅

57 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 2 generators on 33 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 98);