C₂×C₃₇×#384 #17991102

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₃₇×#384

Subgroups

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

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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);(4,6)(8,9)(11,12,13,14);(7,8,10,9);(3,4,5,6)(7,9,10,8)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1296, C₃₇×#8040, C₃₇×#8043, …
maximal normal subgroup of	C₂×C₃₇×#1296, C₃₇×#8040, C₃₇×#8043, …
maximal quotient of	C₂×C₃₇×C₄⋊#95, C₄×C₃₇×#384, C₂×C₃₇×#1444, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1016);

C2×C37×#384 #17991102