Finite Group Databasebeta

← Prev (#34118569) Next (#34118571) →

#34118570

order20202
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC7×C13×C37 ⋊ C2×C3
HallC13×#11715913 ⋊ C2
HallC37×D91 ⋊ C3
Hall#11715913 ⋊ D13
HallC13×C37 ⋊ AGL(1,𝔽7)
HallC7×C37 ⋊ C3×D13
HallD91 ⋊ C37⋊C3
HallC7×C13 ⋊ C2×C37⋊C3
SylowC37 ⋊ ΓL(1,𝔽8)⋊D13
SylowC13 ⋊ #13095535
SylowC7 ⋊ D13×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C37C2×C3
LCSG ▷ C7×C13×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 3367

A minimal faithful permutation representation — 2 generators on 57 points:

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

Polycyclic presentation:

2,3,7,13,37|c^a=c^6,d^a=d^12,c^b=c^2,e^b=e^26

Conjugacy classes & character table

601 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 100);