C₃₇×#1044 #16814880

order	3700
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₅

Aliases

direct product

C₃₇×#1044

Splittings

Fitting, socle, Hall	C₅²×C₃₇ ⋊ C₄
derived, Sylow	C₅² ⋊ C₄×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	#1044
commutator, hypocenter	C₅²	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₅²×C₃₇	C₄
prime radical	C₃₇×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₃₇
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₇

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 370

A minimal faithful permutation representation — 2 generators on 47 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)(40,43,41,45)(42,46,47,44);(39,45,47,42,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#1044×C₃₇⋊C₃, C₃₇×#64480, C₃×C₃₇×#1044, …
maximal normal subgroup of	#1044×C₃₇⋊C₃, C₃×C₃₇×#1044, C₇×C₃₇×#1044
maximal quotient of	C₃×C₃₇×#1044, C₃₇×C₃⋊#1044, C₇×C₃₇×#1044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3700, 34);

C37×#1044 #16814880