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C3×D4945 #44445798

order29670
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4945
unambiguous semidirect productC5⋊(C3×D989)
unambiguous semidirect productC23⋊(C3×D215)

Splittings

Fitting, socle, HallC3×C5×C23×C43 ⋊ C2
derived, HallC5×C23×C43 ⋊ C2×C3
HallC3×C23×C43 ⋊ D5
HallC23×C43 ⋊ C3×D5
HallC3×C5×C43 ⋊ D23
HallC3×C5×C23 ⋊ D43
HallC5×C43 ⋊ C3×D23
HallC3×C43 ⋊ D115
HallC5×C23 ⋊ C3×D43
HallC3×C23 ⋊ D215
SylowC43 ⋊ C3×D115
SylowC23 ⋊ C3×D215
HallC3×C5 ⋊ D989
SylowC5 ⋊ C3×D989

Subgroups

subgroupG/H
center, hypercenterC3D4945
commutator, cosocle, hypocenterC5×C23×C43C2×C3
FrattiniC1G
Fitting, socleC3×C5×C23×C43C2
LCSG ▷ C5×C23×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 74
transitive degreeμt(G) = 14835

A minimal faithful permutation representation — 2 generators on 74 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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(5,8)(6,7)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(33,74)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

7422 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 9);