D₄×#41×C₂₉ #16817182

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄×#41×C₂₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 41 points:

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

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8436, C₂₉×#17507, C₂₉×#17511, …
maximal normal subgroup of	C₂₉×#8436, C₂₉×#17507, C₂₉×#17511, …
maximal quotient of	C₂²⋊C₄×#41×C₂₉, C₄⋊C₄×#41×C₂₉, D₄×C₂₉×#117, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2200);

D4×#41×C29 #16817182