C₂₉×#2530 #16816244

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

Aliases

direct product

C₂₉×#2530

Subgroups

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

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

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)(30,31,33,35)(32,34,36,37)(38,39,41,43)(40,44,45,42)(48,52)(51,53);(30,31,33,35)(32,34,36,37)(38,40,41,45)(39,42,43,44)(46,47,50,49)(48,51,52,53);(30,31)(32,34)(33,35)(36,37)(38,40)(39,42)(41,45)(43,44)(46,48)(47,51)(49,53)(50,52);(30,32,33,36)(31,34,35,37)(38,39)(40,42)(41,43)(44,45)(46,49,50,47)(48,53,52,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2530, C₂₉×#34793, C₂₉×#34806, …
maximal normal subgroup of	C₂×C₂₉×#2530, C₂₉×#34793, C₂₉×#34806, …
maximal quotient of	C₂₉×#13898, C₂₉×#13945, C₂₉×#14011, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1262);

C29×#2530 #16816244