Finite Group Databasebeta

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C2×C3×C5×D437 #39910802

order26220
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D437
unambiguous semidirect product(C2×C23)⋊(C3×C5×D19)

Splittings

Fitting, socleC2×C3×C5×C19×C23 ⋊ C2
derived, HallC19×C23 ⋊ C22×C3×C5
HallC3×C5×C19×C23 ⋊ C22
HallC5×C19×C23 ⋊ C22×C3
HallC3×C19×C23 ⋊ C22×C5
HallC3×C5×C23 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ C2×C3×D19
HallC5×C19 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×C5×D19
HallC3×C19 ⋊ C2×C5×D23
SylowC23 ⋊ C2×C3×C5×D19
SylowC19 ⋊ C2×C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D437
commutator, cosocle, hypocenterC19×C23C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C19×C23C2
LCSG ▷ C19×C23
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13110

Conjugacy classes & character table

6600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 92);