C₂₉×#2383 #16816097

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

Aliases

direct product

C₂₉×#2383

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 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)(30,31,32,33)(35,38)(36,40)(42,43,46,44)(45,48,49,47);(35,38)(39,41)(43,44)(45,49);(34,35)(36,39)(37,38)(40,41)(42,44,46,43)(45,48,49,47);(34,36,37,40)(35,39,38,41)(42,45)(43,47)(44,48)(46,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2383, C₂₉×#34350, C₄×C₂₉×#560, …
maximal normal subgroup of	C₂×C₂₉×#2383, C₂₉×#34350, C₄×C₂₉×#560, …
maximal quotient of	C₂₉×#13830, C₂₉×#13831, C₂₉×#13833, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1115);