C₂₉×#2178 #16815892

order	3712
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2178

Subgroups

	subgroup	G/H
center	C₈×C₂₉	D₈
commutator	C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₄×D₈
prime radical	C₂₉×#508	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

146 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 76 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)(30,31,35,39,36,41,51,40)(32,42,44,53,46,59,45,61)(33,38,47,56,48,57,34,49)(37,52,54,60,55,50,58,43);(30,32)(31,37)(33,43)(34,50)(35,44)(36,46)(38,53)(39,54)(40,58)(41,55)(42,49)(45,51)(47,52)(48,60)(56,59)(57,61);(30,33,35,47,36,48,51,34)(31,38,39,56,41,57,40,49)(32,43,44,52,46,60,45,50)(37,53,54,59,55,61,58,42)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7387, C₂₉×#7388, C₂₉×#12046, …
maximal normal subgroup of	C₂₉×#7387, C₂₉×#7388, C₂₉×#12046, …
maximal quotient of	C₈×C₂₉×D₁₆, C₈×C₂₉×SD₃₂, C₈×C₂₉×Q₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 910);