C₂³×SD₁₆×C₃₇ #17992393

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂³×SD₁₆×C₃₇

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₃₇	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₇
prime radical	C₂³×D₄×C₃₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 5 generators on 51 points:

(1,2)(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);(3,4);(5,6);(7,8,9,10,11,12,13,14);(8,10)(9,13)(12,14)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#11023, C₃₇×#11028, C₂×C₃₇×#1877, …
maximal normal subgroup of	C₃₇×#11023, C₃₇×#11028, C₂×C₃₇×#1877, …
maximal quotient of	C₂³×#102×C₃₇, C₂³×#103×C₃₇, C₂³×#106×C₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2307);

C23×SD16×C37 #17992393