C₃₇×#2513 #17991331

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#2513

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 61 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)(38,39,42,40)(41,44,45,43)(47,50)(48,52)(54,55,58,61)(56,60,57,59);(39,40)(43,44)(46,47,49,50)(48,51,52,53)(54,56,58,57)(55,59,61,60);(38,40,42,39)(41,44,45,43)(46,47)(48,51)(49,50)(52,53)(54,55)(56,59)(57,60)(58,61);(38,41,42,45)(39,43,40,44)(46,48,49,52)(47,51,50,53)(54,57,58,56)(55,60,61,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#27065, C₃₇×#27069, C₃₇×#27072, …
maximal normal subgroup of	C₃₇×#27065, C₃₇×#27069, C₃₇×#27072, …
maximal quotient of	C₃₇×#13885, C₃₇×#13936, C₃₇×#14002, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1245);

C37×#2513 #17991331