C₃₇×#3384 #17992202

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3384

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×D₈×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×Q₈×C₃₇ ◁ G

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 53 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)(38,39,42,41)(40,44,45,43)(47,50)(48,52)(51,53);(38,40,42,45)(39,43,41,44)(47,51)(50,53);(46,47)(48,53)(49,51)(50,52);(38,41,42,39)(40,43,45,44)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#19763, C₃₇×#19766, C₃₇×#19811, …
maximal normal subgroup of	C₃₇×#19763, C₃₇×#19766, C₃₇×#19811, …
maximal quotient of	C₃₇×#22522, C₃₇×#22523, C₃₇×#22670, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2116);

C37×#3384 #17992202