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C3×C7×C31⋊AGL(1,𝔽5) #27189221

order13020
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C31⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C31 ⋊ C4
derived, HallC5×C31 ⋊ C3×C4×C7
HallC5×C7×C31 ⋊ C3×C4
HallC3×C7×C31 ⋊ AGL(1,𝔽5)
HallC3×C5×C31 ⋊ C4×C7
HallC7×C31 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic31
HallC3×C31 ⋊ C7×AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic31
SylowC31 ⋊ C3×C7×AGL(1,𝔽5)
HallC3×C5 ⋊ C7×Dic31
SylowC5 ⋊ C3×C7×Dic31

Subgroups

subgroupG/H
center, hypercenterC3×C7C31⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C31C4
prime radicalC3×C7×D5×C31C2
cosocleD5×C31C2×C3×C7
LCSG ▷ C5×C31
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 3255

A minimal faithful permutation representation — 2 generators on 46 points:

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

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 188);