Finite Group Databasebeta

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C3×C11×D413 #41030656

order27258
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D413
unambiguous semidirect productC59⋊(C3×C11×D7)

Splittings

Fitting, socle, HallC3×C7×C11×C59 ⋊ C2
derived, HallC7×C59 ⋊ C2×C3×C11
HallC7×C11×C59 ⋊ C2×C3
HallC3×C11×C59 ⋊ D7
HallC3×C7×C59 ⋊ C2×C11
HallC11×C59 ⋊ C3×D7
HallC3×C7×C11 ⋊ D59
HallC3×C59 ⋊ C11×D7
HallC7×C11 ⋊ C3×D59
SylowC59 ⋊ C3×C11×D7
HallC3×C7 ⋊ C11×D59
SylowC7 ⋊ C3×C11×D59

Subgroups

subgroupG/H
center, hypercenterC3×C11D413
commutator, cosocle, hypocenterC7×C59C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C59C2
LCSG ▷ C7×C59
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13629

Conjugacy classes & character table

6864 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27258, 7);