Finite Group Databasebeta

← Prev (#41004681) Next (#41004683) →

H(3,𝔽3)2×C37 #41004682

order26973
nilpotency class2
automorphism?
homologyAbelianization (H1) = C34×C37 · Schur multiplier (H2) = C38

Aliases

direct productH(3,𝔽3)2×C37

Subgroups

subgroupG/H
center, socleC32×C37C34
commutator, Frattini, cosocleC32C34×C37
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C37 ◁ G

2102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 2997

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

(1,2,4)(3,6,8)(5,9,7)(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)(14,18,16);(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, 453);