C₂₉×#2191 #16815905

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2191

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#575	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×M₁₆×C₂₉ ◁ G

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

normal subgroups only

This group has 216 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) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 3 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)(30,31,35,39)(32,40,42,58)(33,44,46,60)(34,49,47,38)(36,51,52,41)(37,54,56,48)(43,59,50,55)(45,57,61,53);(30,32)(31,36)(33,45)(34,50)(35,42)(37,55)(38,57)(39,52)(40,44)(41,48)(43,47)(46,61)(49,53)(51,54)(56,59)(58,60);(33,46)(37,56)(40,58)(41,51)(44,60)(45,61)(48,54)(55,59)

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12115, C₂₉×#12116, C₂₉×#12118, …
maximal normal subgroup of	C₂₉×#12115, C₂₉×#12116, C₂₉×#12118, …
maximal quotient of	C₂₉×#12105, C₂₉×#12106, C₂₉×#12107, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 923);