C₃₇×#1379 #17990197

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1379

Subgroups

	subgroup	G/H
center	C₂×C₈×C₃₇	D₄
commutator	C₄	C₄×C₈×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂³×C₃₇	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

136 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 73
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 73 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)(42,43,46,51,47,52,61,69,48,53,62,70,45,50,59,67)(44,54,56,71,55,65,72,68,57,66,60,73,58,49,63,64);(38,39,40,41)(42,44)(43,49)(45,58)(46,60)(47,55)(48,57)(50,66)(51,68)(52,54)(53,65)(56,62)(59,72)(61,63)(64,70)(67,71)(69,73)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1379, C₃₇×#12554, C₃₇×#12597, …
maximal normal subgroup of	C₂×C₃₇×#1379, C₃₇×#12554, C₃₇×#12597, …
maximal quotient of	C₃₇×#7141, C₃₇×#7144, C₃₇×#7147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 111);