C₂³×D₄×C₃₇ #14557245

order	2368
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product	C₂³×D₄×C₃₇
unambiguous semidirect product	C₄⋊(C₂⁴×C₃₇)
unambiguous semidirect product	C₂²⋊(C₂⁴×C₃₇)

	subgroup	G/H
center, socle	C₂⁴×C₃₇	C₂²
commutator, Frattini, cosocle	C₂	C₂⁵×C₃₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ G

1362 conjugacy classes of subgroups.

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 47 points:

(1,2)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4);(5,6);(7,8,9,10);(8,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 261);