Finite Group Databasebeta

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C4×C19⋊C3×C121 #42119913

order27588
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC4×C19⋊C3×C121
unambiguous semidirect product(C4×C19)⋊(C3×C121)
unambiguous semidirect product(C4×C19×C121)⋊C3

Splittings

Fitting, HallC4×C19×C121 ⋊ C3
derived, SylowC19 ⋊ C3×C4×C121
HallC19×C121 ⋊ C3×C4
HallC4×C19 ⋊ C3×C121

Subgroups

subgroupG/H
center, hypercenterC4×C121C19⋊C3
commutator, hypocenterC19C3×C4×C121
FrattiniC2×C11C2×C11×C19⋊C3
FittingC4×C19×C121C3
socle, cosocleC2×C11×C19C2×C3×C11
prime radicalC2×C11×C19⋊C3C2×C11
LCSG ▷ C19
UCSC1 ◁ C4×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9196

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 5);