Finite Group Databasebeta

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C11×C19×Dic33 #42119963

order27588
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC11×C19×Dic33
unambiguous semidirect productC3⋊(C11×C19×Dic11)
unambiguous semidirect productC11⋊(C11×Dic3×C19)

Splittings

derivedC3×C11 ⋊ C4×C11×C19
HallC3×C112×C19 ⋊ C4
HallC112×C19 ⋊ Dic3
HallC3×C112 ⋊ C4×C19
SylowC112 ⋊ Dic3×C19
HallC3×C19 ⋊ C11×Dic11
SylowC3 ⋊ C11×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D33
commutator, hypocenterC3×C11C4×C11×C19
FrattiniC2C11×C19×D33
Fitting, socle, prime radicalC2×C3×C112×C19C2
cosocleC2×C3×C11C2×C11×C19
LCSG ▷ C3×C11
UCSC1 ◁ C2×C11×C19

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

7524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 55);