C₃₇×#3458 #17992276

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3458

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂⁵
prime radical	C₂⁴×C₃₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 61 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)(38,39,41,43)(40,44,45,42)(46,47)(48,54)(49,53)(50,52)(51,55)(56,60)(57,59)(58,61);(46,48)(47,51)(49,56)(50,55)(52,54)(53,58)(57,61)(59,60);(38,40,41,45)(39,42,43,44)(48,55)(51,54)(56,61)(58,60);(47,52)(51,54)(53,59)(58,60);(46,49,50,57)(47,53,52,59)(48,56,55,61)(51,58,54,60)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8410, C₃₇×#11389, C₃₇×#11391, …
maximal normal subgroup of	C₃₇×#8410, C₃₇×#11389, C₃₇×#11391, …
maximal quotient of	C₃₇×#34052, C₃₇×#34074, C₄×C₃₇×#543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2190);

C37×#3458 #17992276