C₂×#4558 #71993

order	384
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

392 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 25 points:

(3,4,5)(6,7)(8,9)(10,12,13,21,15,22,14,23)(11,16,17,20,19,24,18,25);(4,5)(7,9)(10,11,14,18,15,19,13,17)(12,20,21,24,22,25,23,16);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 4569);