C₂×C₂₉×#563 #16817242

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×#563

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 55 points:

(1,2)(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);(4,7)(5,9)(11,12,16,14)(13,19,21,17)(15,22,24,18)(20,25,23,26);(4,7)(8,10)(11,13,16,21)(12,17,14,19)(15,23,24,20)(18,26,22,25);(3,4)(5,8)(6,7)(9,10)(11,14,16,12)(13,17,21,19)(15,22,24,18)(20,25,23,26);(3,5)(4,8)(6,9)(7,10)(11,15)(12,18)(13,20)(14,22)(16,24)(17,25)(19,26)(21,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8507, C₂₉×#12764, C₂₉×#12775, …
maximal normal subgroup of	C₂₉×#8507, C₂₉×#12764, C₂₉×#12775, …
maximal quotient of	C₂×C₂₉×#2376, C₂×C₂₉×#2378, C₂×C₂₉×#2379, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2260);

C2×C29×#563 #16817242