C₂⁵×C₄×C₃₇ #17992405

order	4736
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 737232814080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵

Aliases

abelian

C₂⁵×C₄×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₃₇
socle, prime radical	C₂⁶×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

10552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 6 generators on 51 points:

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

Conjugacy classes & character table

4736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×C₂²⋊#95, C₄×C₃₇×#379, C₃₇×#14680, …
maximal normal subgroup of	C₂×C₃₇×C₂²⋊#95, C₄×C₃₇×#379, C₃₇×#14680, …
maximal quotient of	C₂⁴×C₂²⋊C₄×C₃₇, C₂⁴×C₄⋊C₄×C₃₇, C₂³×#117×C₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2319);

C25×C4×C37 #17992405