C₃₇×#10624896 #41004685

order	26973
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₃⁴×C₃₇ · Schur multiplier (H₂) = C₃⁶

Aliases

direct product

C₃₇×#10624896

Subgroups

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₃₇
prime radical	C₃₇×C₃²⋊H(3,𝔽₃)	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ G

1082 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

normal subgroups only

This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 482 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 — 4 generators on 73 points:

(1,2,4)(3,6,8)(5,9,7)(10,11,14,13,16,23,21,27,34)(12,17,28,20,26,22,19,15,24)(18,30,35,31,25,36,32,29,33)(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);(10,12,18,13,20,31,21,19,32)(11,15,25,16,17,29,27,26,30)(14,22,33,23,24,35,34,28,36);(2,5,6)(4,8,9);(12,19,20)(15,26,17)(18,31,32)(22,28,24)(25,29,30)(33,35,36)

Conjugacy classes & character table

4477 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 456);