Finite Group Databasebeta

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C3×C11×D371 #37587491

order24486
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D371
unambiguous semidirect productC53⋊(C3×C11×D7)

Splittings

Fitting, socle, HallC3×C7×C11×C53 ⋊ C2
derived, HallC7×C53 ⋊ C2×C3×C11
HallC7×C11×C53 ⋊ C2×C3
HallC3×C11×C53 ⋊ D7
HallC3×C7×C53 ⋊ C2×C11
HallC11×C53 ⋊ C3×D7
HallC3×C7×C11 ⋊ D53
HallC3×C53 ⋊ C11×D7
HallC7×C11 ⋊ C3×D53
SylowC53 ⋊ C3×C11×D7
HallC3×C7 ⋊ C11×D53
SylowC7 ⋊ C3×C11×D53

Subgroups

subgroupG/H
center, hypercenterC3×C11D371
commutator, cosocle, hypocenterC7×C53C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C53C2
LCSG ▷ C7×C53
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12243

Conjugacy classes & character table

6171 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 7);