C₃₇×#1415 #17990233

order	4736
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1415

Subgroups

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

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 2368

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)(42,43)(44,48)(45,57)(46,60)(47,52)(49,53)(50,54)(51,58)(55,67)(56,63)(59,73)(61,69)(62,68)(64,72)(65,70)(66,71);(43,48)(44,53)(45,54)(46,58)(49,50)(51,67)(52,63)(55,72)(56,70)(57,61)(59,71)(60,62)(64,73)(65,66)(68,69)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1415, C₃₇×#13615, C₃₇×#13616, …
maximal normal subgroup of	C₂×C₃₇×#1415, C₃₇×#13615, C₃₇×#13616, …
maximal quotient of	C₃₇×#7383, C₃₇×#7418, C₃₇×#7444, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 147);

C37×#1415 #17990233