Finite Group Databasebeta

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D3×C7×C11×C53 #37587494

order24486
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C11×C53
unambiguous semidirect productC3⋊(C2×C7×C11×C53)

Splittings

Fitting, socle, HallC3×C7×C11×C53 ⋊ C2
derived, SylowC3 ⋊ C2×C7×C11×C53
HallC3×C11×C53 ⋊ C2×C7
HallC3×C7×C53 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C53
HallC3×C53 ⋊ C2×C7×C11
HallC3×C11 ⋊ C2×C7×C53
HallC3×C7 ⋊ C2×C11×C53

Subgroups

subgroupG/H
center, hypercenterC7×C11×C53D3
commutator, cosocle, hypocenterC3C2×C7×C11×C53
FrattiniC1G
Fitting, socleC3×C7×C11×C53C2
LCSG ▷ C3
UCSC1 ◁ C7×C11×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12243

Conjugacy classes & character table

12243 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 10);