#433×C₇₃ #17988152

order	4672
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

#433×C₇₃

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 2336

A minimal faithful permutation representation — 3 generators on 97 points:

(1,2)(3,6)(4,5)(7,8)(9,10,12,15,13,16,19,22)(11,14,18,21,17,20,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,5)(6,8)(9,11)(10,14)(12,18)(13,17)(15,21)(16,20)(19,23)(22,24);(1,3,4,7)(2,6,5,8)(11,17)(14,20)(18,23)(21,24)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#34014402, #34014403, #34014408, …
maximal subgroup of	C₂×#433×C₇₃, C₇₃×#2921, C₇₃×#2922, …
maximal normal subgroup of	C₂×#433×C₇₃, C₇₃×#2921, C₇₃×#2922, …
maximal quotient of	C₇₃×#1746, C₇₃×#1750, C₇₃×#1768, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 114);

#433×C73 #17988152