3₋¹⁺²²×C₃₇ #41004687

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

Aliases

direct product

3₋¹⁺²²×C₃₇

Subgroups

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ G

836 conjugacy classes of subgroups; only the 518 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 518 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) = 55
transitive degree	μ_t(G) = 2997

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2,4,3,6,8,7,5,9)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(2,5,6)(4,8,9);(10,11,13,12,15,17,16,14,18);(11,14,15)(13,17,18)

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, 458);