Finite Group Databasebeta

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C3×C53×D115 #49143261

order36570
automorphism?
homologyAbelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1

Aliases

direct productC3×C53×D115
unambiguous semidirect productC5⋊(C3×D23×C53)
unambiguous semidirect productC23⋊(C3×D5×C53)

Splittings

Fitting, socle, HallC3×C5×C23×C53 ⋊ C2
derived, HallC5×C23 ⋊ C2×C3×C53
HallC5×C23×C53 ⋊ C2×C3
HallC3×C23×C53 ⋊ D5
HallC23×C53 ⋊ C3×D5
HallC3×C5×C53 ⋊ D23
HallC3×C5×C23 ⋊ C2×C53
HallC5×C53 ⋊ C3×D23
HallC3×C23 ⋊ D5×C53
SylowC23 ⋊ C3×D5×C53
HallC3×C5 ⋊ D23×C53
SylowC5 ⋊ C3×D23×C53

Subgroups

subgroupG/H
center, hypercenterC3×C53D115
commutator, cosocle, hypocenterC5×C23C2×C3×C53
FrattiniC1G
Fitting, socleC3×C5×C23×C53C2
LCSG ▷ C5×C23
UCSC1 ◁ C3×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18285

Conjugacy classes & character table

9381 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36570, 7);