Finite Group Databasebeta

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C7×C13×C23⋊C11 #37527730

order23023
automorphism?
homologyAbelianization (H1) = C7×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×C23⋊C11
unambiguous semidirect productC23⋊(C7×C11×C13)
unambiguous semidirect product(C7×C23)⋊(C11×C13)
unambiguous semidirect product(C13×C23)⋊(C7×C11)
unambiguous semidirect product(C7×C13×C23)⋊C11

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C11
derived, SylowC23 ⋊ C7×C11×C13
HallC13×C23 ⋊ C7×C11
HallC7×C23 ⋊ C11×C13

Subgroups

subgroupG/H
center, hypercenterC7×C13C23⋊C11
commutator, cosocle, hypocenterC23C7×C11×C13
FrattiniC1G
Fitting, socleC7×C13×C23C11
LCSG ▷ C23
UCSC1 ◁ C7×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

1183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23023, 2);