C₄×#97×C₃₇ #17990543

order	4736
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄³×C₃₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₄×#97×C₃₇

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₃₇	C₂²
commutator	C₂	C₄³×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₃₇ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 53 points:

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

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7019, C₃₇×#7030, C₃₇×#7149, …
maximal normal subgroup of	C₃₇×#7019, C₃₇×#7030, C₃₇×#7149, …
maximal quotient of	C₄×C₃₇×#322, C₈×#97×C₃₇, C₃₇×#7842, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 457);

C4×#97×C37 #17990543