C₂₉×#2502 #16816216

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2502

Subgroups

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

544 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 248 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 — 4 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)(36,40)(37,39)(38,41)(42,43,46,49)(44,48,45,47);(34,35,37,39)(36,38,41,40)(42,44,46,45)(43,47,49,48);(30,31,32,33)(34,35)(36,38)(37,39)(40,41);(34,36,37,41)(35,38,39,40)(42,45,46,44)(43,48,49,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9461, C₂₉×#9951, C₂₉×#9959, …
maximal normal subgroup of	C₂₉×#9461, C₂₉×#9951, C₂₉×#9959, …
maximal quotient of	C₂₉×#13880, C₂₉×#13924, C₂₉×#14000, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1234);