C₃₇×#2981 #17991799

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

Aliases

direct product

C₃₇×#2981

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 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)(40,44)(41,43)(42,45)(46,47,50,54,49,53,57,61)(48,52,56,60,55,51,58,59);(38,40)(39,42)(41,45)(43,44)(46,48)(47,51)(49,55)(50,56)(52,53)(54,59)(57,58)(60,61);(40,45)(42,44)(46,48)(47,52)(49,55)(50,56)(51,53)(54,60)(57,58)(59,61);(39,43)(42,44)(47,53)(48,55)(54,61)(56,58)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9279, C₃₇×#9281, C₃₇×#9283, …
maximal normal subgroup of	C₃₇×#9279, C₃₇×#9281, C₃₇×#9283, …
maximal quotient of	C₃₇×#20531, C₃₇×#20537, C₃₇×#20565, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1713);

C37×#2981 #17991799