C₂₉×#3407 #16817121

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3407

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₂⁴
commutator	C₂	C₂³×C₈×C₂₉
Frattini, cosocle	C₈	C₂⁴×C₂₉
socle	C₂×C₂₉	C₂³×C₈
prime radical	C₂×#41×C₂₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,33,38,34,39,43,51,35,37,44,49,45,50,55,59)(32,36,41,47,42,48,54,58,40,46,52,56,53,57,60,61);(30,32)(31,36)(33,41)(34,42)(35,40)(37,46)(38,47)(39,48)(43,54)(44,52)(45,53)(49,56)(50,57)(51,58)(55,60)(59,61);(32,40)(36,46)(41,52)(42,53)(47,56)(48,57)(54,60)(58,61);(31,37)(36,46)(38,49)(39,50)(47,56)(48,57)(51,59)(58,61)

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#12618, C₂₉×#12833, C₂₉×#12915, …
maximal normal subgroup of	C₂₉×#12618, C₂₉×#12833, C₂₉×#12915, …
maximal quotient of	C₂₉×#33324, C₂₉×#33326, C₂₉×#33333, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2139);

C29×#3407 #16817121