C₂×C₂₉×#564 #16817244

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×#564

Subgroups

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

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 5 generators on 63 points:

(1,2)(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);(5,11)(6,14)(8,12)(9,16)(19,20,23,26)(21,24,29,27)(22,30,31,25)(28,33,34,32);(3,4,7,10)(5,12,11,8)(6,9,14,16)(13,18,17,15)(19,20)(21,27)(22,30)(23,26)(24,29)(25,31)(28,32)(33,34);(3,5,7,11)(4,8,10,12)(6,13,14,17)(9,15,16,18)(19,21)(20,24)(22,28)(23,29)(25,32)(26,27)(30,33)(31,34);(3,6)(4,9)(5,13)(7,14)(8,15)(10,16)(11,17)(12,18)(19,22,23,31)(20,25,26,30)(21,28,29,34)(24,32,27,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8509, C₂×C₂₉×#1658, C₂×C₂₉×#1663, …
maximal normal subgroup of	C₂₉×#8509, C₂×C₂₉×#1658, C₂×C₂₉×#1663, …
maximal quotient of	C₂×C₂₉×#2382, C₄×C₂₉×#564, C₂×C₂₉×#2839, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2262);

C2×C29×#564 #16817244