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C3×D3145 #34038268

order18870
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3145
unambiguous semidirect productC5⋊(C3×D629)
unambiguous semidirect productC17⋊(C3×D185)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, HallC5×C17×C37 ⋊ C2×C3
HallC3×C17×C37 ⋊ D5
HallC17×C37 ⋊ C3×D5
HallC3×C5×C37 ⋊ D17
HallC3×C5×C17 ⋊ D37
HallC5×C37 ⋊ C3×D17
HallC3×C37 ⋊ D85
HallC5×C17 ⋊ C3×D37
HallC3×C17 ⋊ D185
SylowC37 ⋊ C3×D85
SylowC17 ⋊ C3×D185
HallC3×C5 ⋊ D629
SylowC5 ⋊ C3×D629

Subgroups

subgroupG/H
center, hypercenterC3D3145
commutator, cosocle, hypocenterC5×C17×C37C2×C3
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C5×C17×C37
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 9435

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(5,8)(6,7)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

4722 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#27160370, C3×#27160371, C3×#27160374, …
maximal normal subgroup ofC3×#27160370, C3×#27160371, C3×#27160374, …
maximal quotient ofC3×Dic3145, C2×C3×D3145

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 9);