C₂×#131×C₃₇ #14557232

order	2368
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#131×C₃₇

Subgroups

	subgroup	G/H
center	C₂×C₈×C₃₇	C₂²
commutator	C₂	C₂³×C₄×C₃₇
Frattini, cosocle	C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂²×C₄
prime radical	C₂×#41×C₃₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₇ ◁ G

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 55 points:

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

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#1757, C₃₇×#1764, C₃₇×#1765, …
maximal normal subgroup of	C₃₇×#1757, C₃₇×#1764, C₃₇×#1765, …
maximal quotient of	C₂×C₃₇×#405, C₄×#131×C₃₇, C₂×C₃₇×#408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 248);

C2×#131×C37 #14557232