Finite Group Databasebeta

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C3×C11×C19×Dic11 #42119969

order27588
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C19×Dic11
unambiguous semidirect productC11⋊(C3×C4×C11×C19)

Splittings

derivedC11 ⋊ C3×C4×C11×C19
HallC3×C112×C19 ⋊ C4
HallC112×C19 ⋊ C3×C4
HallC3×C112 ⋊ C4×C19
SylowC112 ⋊ C3×C4×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C19D11
commutator, hypocenterC11C3×C4×C11×C19
FrattiniC2C3×C11×C19×D11
Fitting, socle, prime radicalC2×C3×C112×C19C2
cosocleC2×C11C2×C3×C11×C19
LCSG ▷ C11
UCSC1 ◁ C2×C3×C11×C19

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

8778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 61);