C₃₇×#1423 #17990241

order	4736
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#1423

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	D₁₆
commutator	C₁₆	C₂×C₄×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄×C₃₇ ◁ C₂×C₈×C₃₇ ◁ C₂×C₁₆×C₃₇ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 2 generators on 73 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,40,41)(43,48)(44,49)(45,53)(46,56)(50,65)(51,68)(52,61)(54,70)(55,64)(57,69)(58,59)(60,66)(62,63)(67,73)(71,72);(42,43,49,59,45,50,62,68,56,66,70,73,69,71,55,61,47,52,64,72,57,67,54,60,46,51,63,65,53,58,44,48)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7537, C₃₇×#7538, C₃₇×#7545, …
maximal normal subgroup of	C₃₇×#7537, C₃₇×#7538, C₃₇×#7545, …
maximal quotient of	C₃₇×#7460, C₃₇×#7471, C₃₇×#7545, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 155);

C37×#1423 #17990241