Finite Group Databasebeta

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C23×C29×D15 #34093404

order20010
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C23×C29 · Schur multiplier (H2) = C1

Aliases

direct productC23×C29×D15
unambiguous semidirect productC3⋊(D5×C23×C29)
unambiguous semidirect productC5⋊(D3×C23×C29)

Splittings

Fitting, socle, HallC3×C5×C23×C29 ⋊ C2
derived, HallC3×C5 ⋊ C2×C23×C29
HallC5×C23×C29 ⋊ D3
HallC3×C23×C29 ⋊ D5
HallC3×C5×C29 ⋊ C2×C23
HallC3×C5×C23 ⋊ C2×C29
HallC5×C29 ⋊ D3×C23
HallC5×C23 ⋊ D3×C29
HallC3×C29 ⋊ D5×C23
HallC3×C23 ⋊ D5×C29
SylowC5 ⋊ D3×C23×C29
SylowC3 ⋊ D5×C23×C29

Subgroups

subgroupG/H
center, hypercenterC23×C29D15
commutator, cosocle, hypocenterC3×C5C2×C23×C29
FrattiniC1G
Fitting, socleC3×C5×C23×C29C2
LCSG ▷ C3×C5
UCSC1 ◁ C23×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 10005

A minimal faithful permutation representation — 2 generators on 60 points:

(2,3)(4,5)(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);(1,2,4,5,3)(6,7,8)

Conjugacy classes & character table

6003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20010, 13);