C₄₇×D₄₉ #17987191

order	4606
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×D₄₉
unambiguous semidirect product	C₄₉⋊(C₂×C₄₇)

Splittings

Fitting, Hall	C₄₇×C₄₉ ⋊ C₂
derived, Sylow	C₄₉ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₄₇
Frattini	C₇	D₇×C₄₇
Fitting	C₄₇×C₄₉	C₂
socle	C₇×C₄₇	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₄₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 2303

A minimal faithful permutation representation — 2 generators on 96 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)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96);(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73)

Conjugacy classes & character table

1222 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×D₄₉⋊C₃, C₃×C₄₇×D₄₉, C₄₇×D₁₄₇, …
maximal normal subgroup of	C₄₇×D₄₉⋊C₃, C₃×C₄₇×D₄₉, C₅×C₄₇×D₄₉
maximal quotient of	C₃×C₄₇×D₄₉, C₄₇×D₁₄₇, C₅×C₄₇×D₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4606, 2);

C47×D49 #17987191