Finite Group Databasebeta

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C23×D555 #38784287

order25530
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D555
unambiguous semidirect productC3⋊(C23×D185)
unambiguous semidirect productC5⋊(C23×D111)
unambiguous semidirect productC37⋊(C23×D15)

Splittings

Fitting, socle, HallC3×C5×C23×C37 ⋊ C2
derived, HallC3×C5×C37 ⋊ C2×C23
HallC5×C23×C37 ⋊ D3
HallC3×C23×C37 ⋊ D5
HallC23×C37 ⋊ D15
HallC3×C5×C23 ⋊ D37
HallC5×C37 ⋊ D3×C23
HallC5×C23 ⋊ D111
HallC3×C37 ⋊ D5×C23
HallC3×C23 ⋊ D185
SylowC37 ⋊ C23×D15
HallC3×C5 ⋊ C23×D37
SylowC5 ⋊ C23×D111
SylowC3 ⋊ C23×D185

Subgroups

subgroupG/H
center, hypercenterC23D555
commutator, cosocle, hypocenterC3×C5×C37C2×C23
FrattiniC1G
Fitting, socleC3×C5×C23×C37C2
LCSG ▷ C3×C5×C37
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12765

Conjugacy classes & character table

6417 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25530, 15);