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C3×D7×D155 #27189227

order13020
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D155

Splittings

Fitting, socle, HallC3×C5×C7×C31 ⋊ C22
derived, HallC5×C7×C31 ⋊ C22×C3
HallC3×C7×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C2×D7
HallC7×C31 ⋊ C2×C3×D5
HallC5×C31 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C2×D31
HallC3×C31 ⋊ D5×D7
HallC5×C7 ⋊ C2×C3×D31
SylowC31 ⋊ C3×D5×D7
HallC3×C7 ⋊ C2×D155
HallC3×C5 ⋊ D7×D31
SylowC7 ⋊ C2×C3×D155
SylowC5 ⋊ C3×D7×D31

Subgroups

subgroupG/H
center, hypercenterC3D7×D155
commutator, cosocle, hypocenterC5×C7×C31C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C31C22
LCSG ▷ C5×C7×C31
UCSC1 ◁ C3

80 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)(37,38,40,42,43,41,39)(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)(32,33,35,36,34)(38,39)(40,41)(42,43)

Conjugacy classes & character table

1185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 194);