C₂²×D₁₆×C₃₇ #17992226

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂²×D₁₆×C₃₇

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₃₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 57 points:

(1,2)(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);(3,4);(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20);(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13012, C₃₇×#13017, C₃₇×#13235, …
maximal normal subgroup of	C₃₇×#13012, C₃₇×#13017, C₃₇×#13235, …
maximal quotient of	C₂²×C₃₇×#357, C₂²×C₃₇×#366, C₂×C₄×D₁₆×C₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2140);

C22×D16×C37 #17992226