C₃₇×#10624797 #41004586

order	26973
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₃₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₃₇×#10624797

Subgroups

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
prime radical	C₃×C₃₇×AΣL(1,𝔽₂₇)	C₃
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ C₃²×C₉×C₃₇ ◁ G

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 2997

A minimal faithful permutation representation — 3 generators on 73 points:

(2,4,7)(5,9,8)(10,11,15,13,18,23,14,16,25)(12,19,28,21,17,24,22,27,32)(20,29,33,30,26,34,31,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,2,5,3,4,8,6,7,9)(11,16,18)(15,23,25)(17,19,27)(24,32,28)(26,29,35)(33,34,36);(10,12,20)(11,17,26)(13,21,30)(14,22,31)(15,24,33)(16,19,29)(18,27,35)(23,32,34)(25,28,36)

Conjugacy classes & character table

2701 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 357);