C₂₉×#2861 #16816575

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2861

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

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

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 4 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)(31,33)(35,38)(39,41)(43,45)(47,48);(34,35)(36,39)(37,38)(40,41)(42,43,46,45)(44,47,49,48);(30,31,32,33)(34,35)(36,39)(37,38)(40,41)(42,44,46,49)(43,47,45,48);(34,36,37,40)(35,39,38,41)(42,45,46,43)(44,48,49,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7656, C₂₉×#7676, C₂₉×#7696, …
maximal normal subgroup of	C₂₉×#7656, C₂₉×#7676, C₂₉×#7696, …
maximal quotient of	C₂₉×#14689, C₂₉×#14700, C₂₉×#14701, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1593);