Finite Group Databasebeta

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C23×D455 #35230189

order20930
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D455
unambiguous semidirect productC5⋊(C23×D91)
unambiguous semidirect productC7⋊(C23×D65)
unambiguous semidirect productC13⋊(C23×D35)

Splittings

Fitting, socle, HallC5×C7×C13×C23 ⋊ C2
derived, HallC5×C7×C13 ⋊ C2×C23
HallC7×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D7
HallC5×C7×C23 ⋊ D13
HallC13×C23 ⋊ D35
HallC7×C23 ⋊ D65
HallC5×C23 ⋊ D91
HallC7×C13 ⋊ D5×C23
HallC5×C13 ⋊ D7×C23
HallC5×C7 ⋊ C23×D13
SylowC13 ⋊ C23×D35
SylowC7 ⋊ C23×D65
SylowC5 ⋊ C23×D91

Subgroups

subgroupG/H
center, hypercenterC23D455
commutator, cosocle, hypocenterC5×C7×C13C2×C23
FrattiniC1G
Fitting, socleC5×C7×C13×C23C2
LCSG ▷ C5×C7×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10465

Conjugacy classes & character table

5267 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20930, 15);