C₂₉×#2215 #16815929

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2215

Subgroups

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

174 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 49 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)(32,33)(35,39)(36,40)(37,43)(41,49)(42,47)(44,48)(45,46);(34,35,40,46,37,41,44,47,38,42,48,49,43,45,36,39);(31,33)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7418, C₂₉×#7420, C₂₉×#13661, …
maximal normal subgroup of	C₂₉×#7418, C₂₉×#7420, C₂₉×#13661, …
maximal quotient of	C₂₉×#12430, C₂₉×#12439, C₂₉×#12451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 947);