C₂³×Q₁₆×C₂₉ #16817290

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂³×Q₁₆×C₂₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 5 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4);(5,6);(7,8,9,10,11,12,13,14)(15,22,21,20,19,18,17,16);(7,15,11,19)(8,16,12,20)(9,17,13,21)(10,18,14,22)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#11024, C₂₉×#11029, C₂₉×#12732, …
maximal normal subgroup of	C₂₉×#11024, C₂₉×#11029, C₂₉×#12732, …
maximal quotient of	C₂³×C₂₉×#103, C₂³×C₂₉×#107, C₂²×C₄×Q₁₆×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2308);

C23×Q16×C29 #16817290