C₃₇×#2616 #17991434

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#2616

Subgroups

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

816 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(43,45)(46,47)(48,50)(49,51)(52,53);(39,41)(43,45)(47,48)(51,52);(38,39)(40,41)(42,43)(44,45)(46,48,50,47)(49,51,53,52);(46,49,50,53)(47,51,48,52)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9931, C₃₇×#9935, C₃₇×#18230, …
maximal normal subgroup of	C₃₇×#9931, C₃₇×#9935, C₃₇×#18230, …
maximal quotient of	C₃₇×#14258, C₃₇×#14264, C₃₇×#14300, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1348);