C₄₇×C₂₇⋊C₃ #16838348

order	3807
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×C₂₇⋊C₃
unambiguous semidirect product	C₂₇⋊(C₃×C₄₇)
unambiguous semidirect product	(C₂₇×C₄₇)⋊C₃

Subgroups

	subgroup	G/H
center	C₉×C₄₇	C₃²
commutator	C₃	C₃×C₉×C₄₇
Frattini, cosocle	C₉	C₃²×C₄₇
socle	C₃×C₄₇	C₃×C₉
prime radical	C₃²×C₄₇	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₄₇ ◁ G

24 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)(48,49,52,50,54,60,56,63,68,51,55,59,57,64,67,65,71,73,58,53,61,66,62,69,72,70,74);(49,53,55)(52,59,61)(54,62,64)(60,67,69)(63,70,71)(68,73,74)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#6869, C₄₇×#6872, C₄₇×#6873, …
maximal normal subgroup of	C₄₇×#6869, C₄₇×#6872, C₄₇×#6873, …
maximal quotient of	C₄₇×#6864, C₄₇×C₃²⋊C₂₇, C₄₇×C₉⋊C₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3807, 6);

C47×C27⋊C3 #16838348