Finite Group Databasebeta

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C23×D645 #44445804

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

Aliases

direct productC23×D645
unambiguous semidirect productC3⋊(C23×D215)
unambiguous semidirect productC5⋊(C23×D129)
unambiguous semidirect productC43⋊(C23×D15)

Splittings

Fitting, socle, HallC3×C5×C23×C43 ⋊ C2
derived, HallC3×C5×C43 ⋊ C2×C23
HallC5×C23×C43 ⋊ D3
HallC3×C23×C43 ⋊ D5
HallC23×C43 ⋊ D15
HallC3×C5×C23 ⋊ D43
HallC5×C43 ⋊ D3×C23
HallC3×C43 ⋊ D5×C23
HallC5×C23 ⋊ D129
HallC3×C23 ⋊ D215
SylowC43 ⋊ C23×D15
HallC3×C5 ⋊ C23×D43
SylowC5 ⋊ C23×D129
SylowC3 ⋊ C23×D215

Subgroups

subgroupG/H
center, hypercenterC23D645
commutator, cosocle, hypocenterC3×C5×C43C2×C23
FrattiniC1G
Fitting, socleC3×C5×C23×C43C2
LCSG ▷ C3×C5×C43
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14835

Conjugacy classes & character table

7452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 15);