C₂×C₂₉×#367 #16815871

order	3712
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₂₉×#367

Subgroups

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

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4,5,6)(8,12)(9,16)(10,17)(13,18)(14,22)(15,21)(19,20);(7,8,13,22,10,14,9,12,11,15,16,20,17,19,18,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7474, C₂₉×#7477, C₄×C₂₉×#367, …
maximal normal subgroup of	C₂₉×#7474, C₂₉×#7477, C₄×C₂₉×#367, …
maximal quotient of	C₂×C₂₉×#1372, C₂₉×#12023, C₂₉×#12033, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 889);

C2×C29×#367 #16815871