C₂×C₂₉×#482 #16816801

order	3712
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₂₉×#482

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4)(5,8)(6,7)(9,10)(12,15)(13,16)(17,18);(4,7)(8,10)(11,12,14,15)(13,16,17,18);(3,5,6,9)(4,8,7,10)(11,13,14,17)(12,16,15,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9242, C₄×C₂₉×#482, C₂₉×#21582, …
maximal normal subgroup of	C₂₉×#9242, C₄×C₂₉×#482, C₂₉×#21582, …
maximal quotient of	C₂×C₂₉×#1825, C₂×C₂₉×#1854, C₂×C₂₉×#1875, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1819);

C2×C29×#482 #16816801