C₃₇×#2150 #17990968

order	4736
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2150

Subgroups

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

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 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)(39,41)(42,43,44,48,45,49,50,55,46,47,51,53,52,54,56,57);(38,39,40,41);(43,47)(48,53)(49,54)(55,57)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7152, C₃₇×#7153, C₃₇×#7168, …
maximal normal subgroup of	C₃₇×#7152, C₃₇×#7153, C₃₇×#7168, …
maximal quotient of	C₃₇×#11996, C₃₇×#12004, C₃₇×#12013, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 882);

C37×#2150 #17990968