Finite Group Databasebeta

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C5×D2451 #37587769

order24510
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2451
unambiguous semidirect productC3⋊(C5×D817)
unambiguous semidirect productC19⋊(C5×D129)
unambiguous semidirect productC43⋊(C5×D57)

Splittings

Fitting, socle, HallC3×C5×C19×C43 ⋊ C2
derived, HallC3×C19×C43 ⋊ C2×C5
HallC5×C19×C43 ⋊ D3
HallC19×C43 ⋊ C5×D3
HallC3×C5×C43 ⋊ D19
HallC3×C5×C19 ⋊ D43
HallC5×C43 ⋊ D57
HallC3×C43 ⋊ C5×D19
HallC5×C19 ⋊ D129
HallC3×C19 ⋊ C5×D43
SylowC43 ⋊ C5×D57
SylowC19 ⋊ C5×D129
HallC3×C5 ⋊ D817
SylowC3 ⋊ C5×D817

Subgroups

subgroupG/H
center, hypercenterC5D2451
commutator, cosocle, hypocenterC3×C19×C43C2×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C43C2
LCSG ▷ C3×C19×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12255

Conjugacy classes & character table

6135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 16);