C₂₉×#3415 #16817129

order	3712
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3415

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₂₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ #41×C₂₉ ◁ C₂₉×#131 ◁ G

370 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 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) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 61 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)(30,31)(32,37)(33,36)(34,47)(35,40)(38,44)(39,45)(41,51)(42,48)(43,57)(46,50)(49,58)(52,56)(53,55)(54,59)(60,61);(31,36)(33,44)(34,45)(37,48)(38,39)(40,50)(42,56)(43,55)(46,58)(47,49)(51,59)(52,53)(54,61)(57,60);(30,32)(31,37)(33,42)(34,43)(35,41)(36,48)(38,52)(39,53)(40,51)(44,56)(45,55)(46,54)(47,57)(49,60)(50,59)(58,61);(32,41)(37,51)(42,54)(43,55)(48,59)(52,60)(53,57)(56,61)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13669, C₂₉×#13671, C₂₉×#33854, …
maximal normal subgroup of	C₂₉×#13669, C₂₉×#13671, C₂₉×#33854, …
maximal quotient of	C₂₉×#33381, C₂₉×#33410, C₂₉×#33454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2147);