C₃₇×#1866 #17990684

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1866

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle	C₂²×C₃₇	C₄×D₄
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

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)(38,39)(40,41)(42,43,47,50,48,45,46,51)(44,52,54,49,56,57,55,53);(39,41)(42,44,47,54,48,56,46,55)(43,49,50,57,45,53,51,52);(42,45)(43,48)(44,53)(46,50)(47,51)(49,56)(52,54)(55,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1866, C₃₇×#20884, C₃₇×#20885, …
maximal normal subgroup of	C₂×C₃₇×#1866, C₃₇×#20884, C₃₇×#20885, …
maximal quotient of	C₃₇×#8843, C₃₇×#8844, C₃₇×#8845, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 598);

C37×#1866 #17990684