C₂₉×#2145 #16815859

order	3712
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2145

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#102
commutator	C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₂×#102
prime radical	C₂×C₂₉×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

224 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 100 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)(32,41,44,58)(33,37)(34,48)(35,40)(36,43,52,60)(38,46)(39,47)(42,57,45,54)(49,56,61,51)(50,53)(55,59);(30,32)(31,36)(33,42)(34,49)(35,44)(37,51)(38,54)(39,56)(40,52)(41,53)(43,59)(45,47)(46,60)(48,58)(50,61)(55,57);(30,33,35,47)(31,37,40,39)(32,42,44,45)(34,46,50,59)(36,51,52,56)(38,53,55,48)(41,57,58,54)(43,49,60,61)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12646, C₂₉×#12649, C₂₉×#12741, …
maximal normal subgroup of	C₂₉×#12646, C₂₉×#12649, C₂₉×#12741, …
maximal quotient of	C₂₉×#11597, C₂₉×#11599, C₂₉×#11600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 877);