C₄₇×#733 #16838352

order	3807
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₇ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₄₇×#733

Subgroups

	subgroup	G/H
center, socle	C₃×C₄₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₄₇
prime radical	C₃²×C₄₇	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₇ ◁ C₃²×C₄₇ ◁ G

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 1269

A minimal faithful permutation representation — 2 generators on 74 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49,52,51,55,61,59,54,65)(50,56,60,58,53,62,69,64,72)(57,67,70,68,66,71,74,63,73);(48,50,57,59,69,74,51,58,68)(49,53,63,54,56,66,55,64,67)(52,60,70,65,72,73,61,62,71)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#6878, C₄₇×#6880, C₄₇×#6881, …
maximal normal subgroup of	C₄₇×#6878, C₄₇×#6880, C₄₇×#6881, …
maximal quotient of	C₄₇×#6858, C₄₇×#6860, C₄₇×#6861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3807, 10);

C47×#733 #16838352