#533×C₇₃ #17988252

order	4672
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

#533×C₇₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₃
socle	C₂²×C₇₃	C₂⁴
prime radical	C₂³×C₇₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 2336

A minimal faithful permutation representation — 4 generators on 89 points:

(1,2)(3,6)(4,5)(7,8)(9,10,12,14)(11,15,16,13)(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);(2,5)(6,8);(9,11,12,16)(10,13,14,15);(1,3,4,7)(2,6,5,8)

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34000131, #34000142, #34000823, …
maximal subgroup of	C₇₃×#1481, C₇₃×#1485, C₇₃×#1493, …
maximal normal subgroup of	C₇₃×#1481, C₇₃×#1485, C₇₃×#1493, …
maximal quotient of	C₇₃×#2285, C₇₃×#2295, C₇₃×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 214);

#533×C73 #17988252