Finite Group Databasebeta

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C5×C11×D345 #49182159

order37950
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D345
unambiguous semidirect productC3⋊(C5×C11×D115)
unambiguous semidirect productC5⋊(C5×C11×D69)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derivedC3×C5×C23 ⋊ C2×C5×C11
HallC52×C11×C23 ⋊ D3
HallC3×C52×C23 ⋊ C2×C11
HallC3×C52×C11 ⋊ D23
HallC3×C11×C23 ⋊ C5×D5
HallC52×C23 ⋊ D3×C11
HallC52×C11 ⋊ D69
HallC11×C23 ⋊ C5×D15
HallC3×C52 ⋊ C11×D23
HallC3×C23 ⋊ C5×D5×C11
HallC3×C11 ⋊ C5×D115
SylowC52 ⋊ C11×D69
SylowC23 ⋊ C5×C11×D15
SylowC3 ⋊ C5×C11×D115

Subgroups

subgroupG/H
center, hypercenterC5×C11D345
commutator, cosocle, hypocenterC3×C5×C23C2×C5×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7590

Conjugacy classes & character table

9570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 96);