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C31⋊C3×C7⋊AGL(1,𝔽5) #27189158

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

Aliases

direct productC31⋊C3×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C7×C31 ⋊ C3×C4
HallC31×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×C7×C31⋊C3 ⋊ C4
HallC7×C31⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C31⋊C3 ⋊ Dic7
HallC7×C31 ⋊ C3×AGL(1,𝔽5)
HallC5×C31 ⋊ C3×Dic7
HallC5×C7 ⋊ C4×C31⋊C3
SylowC31 ⋊ C3×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ AGL(1,𝔽5)×C31⋊C3
SylowC5 ⋊ Dic7×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C31C3×C4
prime radicalC7×D5×C31⋊C3C2
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)(4,5)(6,7)(9,12,11,10)(14,15,17)(16,19,24)(18,22,21)(20,26,33)(23,29,31)(25,27,28)(30,36,40)(32,37,38)(34,41,35)(39,42,43);(1,2,4,6,7,5,3)(8,9,12,10,11)(13,14,16,20,27,17,21,28,35,41,24,31,38,26,34,33,40,43,36,19,25,32,39,42,29,15,18,23,30,37,22)

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 125);