C₂₉×#2825 #16816539

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₂₉×#2825

Subgroups

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

522 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 53 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)(31,34)(35,37)(38,39)(40,43)(41,42)(44,45)(46,47,50,51)(48,52,53,49);(32,36)(35,37)(39,42)(40,44)(48,53)(49,52);(30,31)(32,35)(33,34)(36,37)(38,39)(40,45)(41,42)(43,44)(46,48)(47,49)(50,53)(51,52);(30,32)(31,35)(33,36)(34,37)(38,40)(39,43)(41,44)(42,45)(46,49)(47,48)(50,52)(51,53)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2825, C₂₉×#36670, C₂₉×#36676, …
maximal normal subgroup of	C₂×C₂₉×#2825, C₂₉×#36670, C₂₉×#36676, …
maximal quotient of	C₂₉×#14621, C₂₉×#14637, C₂₉×#14642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1557);