Finite Group Databasebeta

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C23×C5⋊(D43⋊C3) #44445811

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

Aliases

direct productC23×C5⋊(D43⋊C3)
unambiguous semidirect productC5⋊(C23×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(D5×C23)
unambiguous semidirect productD215⋊(C3×C23)
unambiguous semidirect product(C23×D215)⋊C3

Splittings

Fitting, socle, HallC5×C23×C43 ⋊ C2×C3
derived, HallC5×C43 ⋊ C2×C3×C23
HallC5×C23×C43⋊C3 ⋊ C2
HallC23×D215 ⋊ C3
HallC23×C43⋊C3 ⋊ D5
HallC23×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ C2×C23
HallD215 ⋊ C3×C23
HallC43⋊C3 ⋊ D5×C23
HallC5×C23 ⋊ D43⋊C3
SylowC43 ⋊ C3×D5×C23
SylowC5 ⋊ C23×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC23C5⋊(D43⋊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

1081 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 22);