C₃×C₁₃×H(3,𝔽₃) #11760418

order	1053
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₃ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product	C₃×C₁₃×H(3,𝔽₃)
unambiguous semidirect product	C₃²⋊(C₃²×C₁₃)

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₁₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ G

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 351

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

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

429 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1053, 12);