C₂₉×#2378 #16816092

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

Aliases

direct product

C₂₉×#2378

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

464 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)(30,31,32,33)(35,38)(36,40)(42,43)(44,48)(45,47)(46,49);(35,38)(39,41)(42,43,45,47)(44,48,49,46);(34,35)(36,39)(37,38)(40,41)(42,43)(44,46)(45,47)(48,49);(34,36)(35,39)(37,40)(38,41)(42,44,45,49)(43,46,47,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9342, C₂₉×#9344, C₂×C₂₉×#2378, …
maximal normal subgroup of	C₂₉×#9342, C₂₉×#9344, C₂×C₂₉×#2378, …
maximal quotient of	C₂₉×#13828, C₂₉×#13831, C₂₉×#13833, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1110);

C29×#2378 #16816092