C₂₉×#463 #14270758

order	1856
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#463

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₉
prime radical	C₂×D₈×C₂₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 41 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)(31,33)(34,35)(36,38)(37,39)(40,41);(30,31,32,33)(35,38)(39,40);(35,39)(37,41)(38,40)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₂₉×#463, #16828944, #16828954, …
maximal subgroup of	C₂×C₂₉×#463, C₂₉×#3035, C₂₉×#3036, …
maximal normal subgroup of	C₂×C₂₉×#463, C₂₉×#3035, C₂₉×#3036, …
maximal quotient of	C₂₉×#1677, C₂₉×#1679, C₂₉×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1856, 144);