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C53×D231 #37587500

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

Aliases

direct productC53×D231
unambiguous semidirect productC3⋊(C53×D77)
unambiguous semidirect productC7⋊(C53×D33)
unambiguous semidirect productC11⋊(D21×C53)

Splittings

Fitting, socle, HallC3×C7×C11×C53 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C53
HallC7×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ D7
HallC3×C7×C53 ⋊ D11
HallC11×C53 ⋊ D21
HallC7×C53 ⋊ D33
HallC3×C53 ⋊ D77
HallC7×C11 ⋊ D3×C53
HallC3×C11 ⋊ D7×C53
HallC3×C7 ⋊ D11×C53
SylowC11 ⋊ D21×C53
SylowC7 ⋊ C53×D33
SylowC3 ⋊ C53×D77

Subgroups

subgroupG/H
center, hypercenterC53D231
commutator, cosocle, hypocenterC3×C7×C11C2×C53
FrattiniC1G
Fitting, socleC3×C7×C11×C53C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12243

Conjugacy classes & character table

6201 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 16);