C₂²×C₂₉×#126 #16817152

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×#126

Subgroups

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

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8309, C₂₉×#8545, C₂₉×#8556, …
maximal normal subgroup of	C₂₉×#8309, C₂₉×#8545, C₂₉×#8556, …
maximal quotient of	C₂²×C₂₉×#383, C₂²×C₂₉×#387, C₂²×C₂₉×#388, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2170);

C22×C29×#126 #16817152