C₂₉×#2115 #16815829

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2115

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₂×C₂²⋊C₈
prime radical	C₂×#41×C₂₉	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

220 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 116 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)(30,31,33,38,34,39,45,53,35,37,46,50,47,51,58,60)(32,40,42,52,43,54,56,61,41,36,44,48,55,49,57,59);(30,32)(31,36)(33,44)(34,43)(35,41)(37,40)(38,52)(39,49)(42,46)(45,57)(47,55)(48,50)(51,54)(53,61)(56,58)(59,60);(32,41)(36,40)(42,44)(43,55)(48,52)(49,54)(56,57)(59,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7207, C₂₉×#7208, C₂₉×#11483, …
maximal normal subgroup of	C₂₉×#7207, C₂₉×#7208, C₂₉×#11483, …
maximal quotient of	C₂₉×#11419, C₂₉×#11441, C₂₉×#11461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 847);