Finite Group Databasebeta

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C2×C3×D19×C121 #42119936

order27588
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D19×C121

Splittings

FittingC2×C3×C19×C121 ⋊ C2
derived, SylowC19 ⋊ C22×C3×C121
HallC3×C19×C121 ⋊ C22
HallC19×C121 ⋊ C22×C3
HallC3×C19 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C3×C121D19
commutator, hypocenterC19C22×C3×C121
FrattiniC11C2×C3×C11×D19
FittingC2×C3×C19×C121C2
socleC2×C3×C11×C19C2×C11
prime radicalC2×C3×C11×D19C11
cosocleC11×C19C22×C3×C11
LCSG ▷ C19
UCSC1 ◁ C2×C3×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13794

Conjugacy classes & character table

7986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 28);