C₃₇×#2242 #17991060

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃₇×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
prime radical	C₂×D₈×C₃₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 77 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)(40,43)(41,42)(44,45)(46,47)(48,60)(49,54)(50,68)(51,71)(52,72)(53,59)(55,64)(56,61)(57,70)(58,69)(62,74)(63,73)(65,77)(66,76)(67,75);(39,42)(43,45)(46,48,61,66,52,63,70,67,53,64,51,62,69,65,50,49)(47,54,68,77,58,74,71,55,59,75,57,73,72,76,56,60);(38,40,41,44)(39,43,42,45)(46,49,50,65,69,62,51,64,53,67,70,63,52,66,61,48)(47,55,56,74,72,77,57,54,59,60,71,76,58,73,68,75)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2242, C₃₇×#33697, C₃₇×#33702, …
maximal normal subgroup of	C₂×C₃₇×#2242, C₃₇×#33697, C₃₇×#33702, …
maximal quotient of	C₃₇×#12889, C₃₇×#13147, C₃₇×#13148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 974);