C₂²×C₂₉×#125 #16817151

order	3712
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂²×C₂₉×#125

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 5 generators on 49 points:

(1,2)(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);(3,4);(7,11)(9,12)(13,14,16,18)(15,17,19,20);(5,6,8,10)(7,9,11,12)(13,14)(15,17)(16,18)(19,20);(5,7)(6,9)(8,11)(10,12)(13,15,16,19)(14,17,18,20)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8306, C₂₉×#8335, C₂₉×#8554, …
maximal normal subgroup of	C₂₉×#8306, C₂₉×#8335, C₂₉×#8554, …
maximal quotient of	C₂²×C₂₉×#382, C₂²×C₂₉×#387, C₂²×C₂₉×#389, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2169);

C22×C29×#125 #16817151