C₃₇×#2820 #17991638

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2820

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

464 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 57
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#10079, C₃₇×#10082, C₃₇×#10083, …
maximal normal subgroup of	C₃₇×#10079, C₃₇×#10082, C₃₇×#10083, …
maximal quotient of	C₃₇×#14624, C₃₇×#14626, C₃₇×#14628, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1552);