C₅²×SL(2,ℤ/4) #11925463

order	1200
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊(C₄×C₅²)

A₄ ⋊ C₄×C₅²

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 2 generators on 18 points:

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

maximal subgroup of	C₅²×GL(2,ℤ/4), SL(2,ℤ/4)×C₅⋊D₅, #72230250, …
maximal normal subgroup of	C₅²×GL(2,ℤ/4), SL(2,ℤ/4)×C₅⋊D₅, #72230250, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 673);