C₂×C₂₉×#562 #16817241

order	3712
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₂₉×#562

Subgroups

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

1152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 47 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8508, C₂×C₂₉×#1656, C₂×C₂₉×#1661, …
maximal normal subgroup of	C₂₉×#8508, C₂×C₂₉×#1656, C₂×C₂₉×#1661, …
maximal quotient of	C₂×C₂₉×#2376, C₂×C₂₉×#2377, C₂×C₂₉×#2378, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2259);

C2×C29×#562 #16817241