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C7×D1749 #37587497

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

Aliases

direct productC7×D1749
unambiguous semidirect productC3⋊(C7×D583)
unambiguous semidirect productC11⋊(C7×D159)
unambiguous semidirect productC53⋊(C7×D33)

Splittings

Fitting, socle, HallC3×C7×C11×C53 ⋊ C2
derived, HallC3×C11×C53 ⋊ C2×C7
HallC7×C11×C53 ⋊ D3
HallC3×C7×C53 ⋊ D11
HallC11×C53 ⋊ D3×C7
HallC7×C53 ⋊ D33
HallC3×C7×C11 ⋊ D53
HallC3×C53 ⋊ C7×D11
HallC7×C11 ⋊ D159
SylowC53 ⋊ C7×D33
HallC3×C11 ⋊ C7×D53
HallC3×C7 ⋊ D583
SylowC11 ⋊ C7×D159
SylowC3 ⋊ C7×D583

Subgroups

subgroupG/H
center, hypercenterC7D1749
commutator, cosocle, hypocenterC3×C11×C53C2×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C53C2
LCSG ▷ C3×C11×C53
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12243

Conjugacy classes & character table

6132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 13);