Finite Group Databasebeta

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C2×C5×#14578575 #37587758

order24510
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#14578575

Splittings

Fitting, socle, HallC2×C5×C19×C43 ⋊ C3
derived, HallC19×C43 ⋊ C2×C3×C5
HallC5×C19×C43 ⋊ C2×C3
HallC2×C19×C43 ⋊ C3×C5
HallC2×C5×C43 ⋊ C19⋊C3
HallC5×C43 ⋊ C2×C19⋊C3
HallC2×C5×C19 ⋊ C43⋊C3
HallC5×C19 ⋊ C2×C43⋊C3
HallC2×C43 ⋊ C5×C19⋊C3
SylowC43 ⋊ C2×C5×C19⋊C3
HallC2×C19 ⋊ C5×C43⋊C3
SylowC19 ⋊ C2×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#14578575
commutator, cosocle, hypocenterC19×C43C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C19×C43C3
LCSG ▷ C19×C43
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8170

Conjugacy classes & character table

2750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 5);