C₂₉×#2612 #16816326

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#2612

Subgroups

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

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 53 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)(32,36)(33,34)(35,37)(46,47,50,53)(48,52,49,51);(31,34)(35,36)(38,39,41,43)(40,42,44,45)(46,48,50,49)(47,51,53,52);(30,31)(32,35)(33,34)(36,37)(38,39)(40,42)(41,43)(44,45)(46,49,50,48)(47,52,53,51);(30,32,33,37)(31,35,34,36)(38,40,41,44)(39,42,43,45)(46,47)(48,51)(49,52)(50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12182, C₂₉×#12258, C₂×C₂₉×#2612, …
maximal normal subgroup of	C₂₉×#12182, C₂₉×#12258, C₂×C₂₉×#2612, …
maximal quotient of	C₂₉×#13963, C₂₉×#14087, C₂₉×#14088, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1344);

C29×#2612 #16816326