C₃×3₋¹⁺²×C₄₇ #16838355

order	3807
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₃×3₋¹⁺²×C₄₇
unambiguous semidirect product	C₉⋊(C₃²×C₄₇)
unambiguous semidirect product	(C₉×C₄₇)⋊C₃²

Subgroups

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₄₇
prime radical	C₃³×C₄₇	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 1269

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(4,5,7,6,9,11,10,8,12);(5,8,9)(7,11,12)

Conjugacy classes & character table

1551 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#6857, C₄₇×#6858, C₄₇×#6860, …
maximal normal subgroup of	C₄₇×#6857, C₄₇×#6858, C₄₇×#6860, …
maximal quotient of	C₃×C₄₇×C₃²⋊C₉, C₃×C₄₇×C₉⋊C₉, C₉×3₋¹⁺²×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3807, 13);

C3×3−1+2×C47 #16838355