C₃₇×#2853 #17991671

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2853

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 57 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)(39,41)(43,45)(44,48)(51,54)(52,56);(42,43,46,45)(44,47,48,49)(50,51)(52,55)(53,54)(56,57);(42,44)(43,47)(45,49)(46,48);(38,39)(40,41)(42,45,46,43)(44,49,48,47)(50,52,53,56)(51,55,54,57)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#24057, C₃₇×#24113, C₃₇×#34983, …
maximal normal subgroup of	C₃₇×#24057, C₃₇×#24113, C₃₇×#34983, …
maximal quotient of	C₃₇×#14684, C₃₇×#14695, C₃₇×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1585);