C₂₉×#2603 #16816317

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2603

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂₉×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#18280, C₂₉×#18282, C₂×C₂₉×#2603, …
maximal normal subgroup of	C₂₉×#18280, C₂₉×#18282, C₂×C₂₉×#2603, …
maximal quotient of	C₂₉×#13952, C₂₉×#13959, C₂₉×#14075, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1335);

C29×#2603 #16816317