Finite Group Databasebeta

← Prev (#27189153) Next (#27189155) →

AGL(1,𝔽5)×#10620252 #27189154

order13020
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×#10620252

Splittings

Fitting, socle, derived, HallC5×C7×C31 ⋊ C3×C4
HallC7×AGL(1,𝔽5)×C31 ⋊ C3
HallC5×#10620252 ⋊ C4
HallAGL(1,𝔽5)×C31 ⋊ ΓL(1,𝔽8)
HallC7×C31 ⋊ C3×AGL(1,𝔽5)
HallC5×C31 ⋊ C4×ΓL(1,𝔽8)
HallC7×AGL(1,𝔽5) ⋊ C31⋊C3
HallC5×C7 ⋊ C4×C31⋊C3
SylowC31 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ AGL(1,𝔽5)×C31⋊C3
SylowC5 ⋊ C4×#10620252

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C31C3×C4
prime radicalD5×#10620252C2
cosocleC7×D5×C31C2×C3
LCSG ▷ C5×C7×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,21)(11,15,18)(13,19,16)(17,24,27)(20,26,25)(22,28,23)(29,31,30)(33,34,35)(36,38,37)(40,41,42,43);(1,2,4,8,15,3,6,11,17,24,7,13,20,21,27,14,22,29,28,12,18,25,30,31,19,5,9,16,23,26,10)(32,33,34,36,35,37,38)(39,40,41,43,42)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 121);