Finite Group Databasebeta

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D5×C23×C43⋊C3 #44445810

order29670
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productD5×C23×C43⋊C3
unambiguous semidirect productC5⋊(C2×C23×C43⋊C3)
unambiguous semidirect product(D5×C43)⋊(C3×C23)
unambiguous semidirect product(D5×C23×C43)⋊C3

Splittings

Fitting, socle, HallC5×C23×C43 ⋊ C2×C3
derived, HallC5×C43 ⋊ C2×C3×C23
HallC5×C23×C43⋊C3 ⋊ C2
HallD5×C23×C43 ⋊ C3
HallC23×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ C2×C23
HallD5×C43 ⋊ C3×C23
HallC5×C23 ⋊ C2×C43⋊C3
SylowC43 ⋊ C3×D5×C23
SylowC5 ⋊ C2×C23×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC23D5×C43⋊C3
commutator, cosocle, hypocenterC5×C43C2×C3×C23
FrattiniC1G
Fitting, socleC5×C23×C43C2×C3
LCSG ▷ C5×C43
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4945

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 21);