C₂×C₂₉×#346 #16815820

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₂₉×#346

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₂₉	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₂₉ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(7,8,9,13,10,14,15,20,11,12,16,18,17,19,21,22);(3,4,5,6)(8,12)(13,18)(14,19)(20,22)

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7137, C₂₉×#7140, C₂₉×#7156, …
maximal normal subgroup of	C₂₉×#7137, C₂₉×#7140, C₂₉×#7156, …
maximal quotient of	C₂×C₂₉×#1311, C₂×C₂₉×#1312, C₂₉×#11408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 838);

C2×C29×#346 #16815820