C₂×C₃₇×#362 #17990965

order	4736
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₃₇×#362

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	#102
commutator	C₈	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
prime radical	C₂³×C₃₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

216 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 71
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 71 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(3,4,7,11,8,13,23,12)(5,14,16,27,17,31,22,30)(6,18,20,10,21,28,34,29)(9,19,24,15,26,32,25,33);(3,5,8,17)(4,9,13,26)(6,19,21,32)(7,22,23,16)(10,27,29,30)(11,25,12,24)(14,18,31,28)(15,20,33,34)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₃₇×#362, C₃₇×#12648, C₃₇×#12737, …
maximal normal subgroup of	C₄×C₃₇×#362, C₃₇×#12648, C₃₇×#12737, …
maximal quotient of	C₂×C₃₇×#1334, C₃₇×#11600, C₃₇×#11653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 879);