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C5×D2553 #38784285

order25530
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2553
unambiguous semidirect productC3⋊(C5×D851)
unambiguous semidirect productC23⋊(C5×D111)
unambiguous semidirect productC37⋊(C5×D69)

Splittings

Fitting, socle, HallC3×C5×C23×C37 ⋊ C2
derived, HallC3×C23×C37 ⋊ C2×C5
HallC5×C23×C37 ⋊ D3
HallC23×C37 ⋊ C5×D3
HallC3×C5×C37 ⋊ D23
HallC3×C5×C23 ⋊ D37
HallC5×C37 ⋊ D69
HallC5×C23 ⋊ D111
HallC3×C37 ⋊ C5×D23
HallC3×C23 ⋊ C5×D37
SylowC37 ⋊ C5×D69
SylowC23 ⋊ C5×D111
HallC3×C5 ⋊ D851
SylowC3 ⋊ C5×D851

Subgroups

subgroupG/H
center, hypercenterC5D2553
commutator, cosocle, hypocenterC3×C23×C37C2×C5
FrattiniC1G
Fitting, socleC3×C5×C23×C37C2
LCSG ▷ C3×C23×C37
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12765

Conjugacy classes & character table

6390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25530, 13);