Finite Group Databasebeta

D3×C1723⋊C3 #44526549

order31014
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD3×C1723⋊C3
unambiguous semidirect productC3⋊(C2×C1723⋊C3)
unambiguous semidirect product(D3×C1723)⋊C3

Splittings

Fitting, socle, derivedC3×C1723 ⋊ C2×C3
HallC3×C1723⋊C3 ⋊ C2
SylowC1723 ⋊ C3×D3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C1723C2×C3
LCSG ▷ C3×C1723
UCSC1

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 1726
transitive degreeμt(G) = 5169

A minimal faithful permutation representation — 2 generators on 1726 points:

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Conjugacy classes & character table

1731 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31014, 10);