C₄₉×D₄₇ #17987192

order	4606
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₉×D₄₇
unambiguous semidirect product	C₄₇⋊(C₂×C₄₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	D₄₇
commutator, hypocenter	C₄₇	C₂×C₄₉
Frattini	C₇	C₇×D₄₇
Fitting	C₄₇×C₄₉	C₂
socle, cosocle	C₇×C₄₇	C₂×C₇
prime radical	C₇×D₄₇	C₇
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₄₉

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

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄₇×C₄₉⋊C₃, C₃×C₄₉×D₄₇, C₄₉×D₁₄₁, …
maximal normal subgroup of	D₄₇×C₄₉⋊C₃, C₃×C₄₉×D₄₇, C₅×C₄₉×D₄₇
maximal quotient of	C₃×C₄₉×D₄₇, C₄₉×D₁₄₁, C₅×C₄₉×D₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4606, 3);

C49×D47 #17987192