C₄₉×#595 #16809703

order	3332
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄₉×#595

Splittings

Fitting, Hall	C₁₇×C₄₉ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	#595
commutator, hypocenter	C₁₇	C₄×C₄₉
Frattini	C₇	C₇×#595
Fitting	C₁₇×C₄₉	C₄
socle	C₇×C₁₇	C₄×C₇
prime radical, cosocle	C₇×D₁₇	C₂×C₇
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 833

A minimal faithful permutation representation — 2 generators on 66 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)(51,52,53,55)(54,57,58,62)(56,61,59,60)(63,65,66,64);(50,51,54,59,55,60,64,66,62,57,63,65,61,52,56,58,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₄₉×#595, C₄₉×#66775, C₄₉×#66776, …
maximal normal subgroup of	C₅×C₄₉×#595, C₁₁×C₄₉×#595
maximal quotient of	C₅×C₄₉×#595, C₄₉×#66775, C₄₉×#66776, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3332, 6);

C49×#595 #16809703