C₂₉×#2210 #16815924

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2210

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂×C₂₉×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 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)(31,33)(34,35)(36,39)(37,40)(38,46)(41,45)(42,44)(43,47)(48,49);(30,31,32,33)(35,39)(40,47)(41,48)(42,46);(35,40)(37,45)(38,44)(39,47)(41,42)(43,49)(46,48)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2210, C₂₉×#33579, C₂₉×#33580, …
maximal normal subgroup of	C₂×C₂₉×#2210, C₂₉×#33579, C₂₉×#33580, …
maximal quotient of	C₂₉×#12418, C₂₉×#12422, C₂₉×#12428, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 942);