C₃₇×D₅₃ #16840970

order	3922
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₇×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₃₇)

Splittings

Fitting, socle, Hall	C₃₇×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₃₇
Frattini	C₁	G
Fitting, socle	C₃₇×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₃₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 90
transitive degree	μ_t(G) = 1961

A minimal faithful permutation representation — 2 generators on 90 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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90);(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₃₇×D₅₃, C₃₇×D₁₅₉, D₅₃×C₃₇⋊C₃, …
maximal normal subgroup of	C₃×C₃₇×D₅₃, D₅₃×C₃₇⋊C₃, C₅×C₃₇×D₅₃, …
maximal quotient of	C₃×C₃₇×D₅₃, C₃₇×D₁₅₉, C₅×C₃₇×D₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3922, 2);

C37×D53 #16840970