C₁₃×#15141 #15701480

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

1906 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 8129);