Finite Group Databasebeta

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C5×C23×D165 #49182160

order37950
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×D165
unambiguous semidirect productC3⋊(C5×C23×D55)
unambiguous semidirect productC5⋊(C5×C23×D33)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derivedC3×C5×C11 ⋊ C2×C5×C23
HallC52×C11×C23 ⋊ D3
HallC3×C52×C23 ⋊ D11
HallC3×C52×C11 ⋊ C2×C23
HallC3×C11×C23 ⋊ C5×D5
HallC52×C23 ⋊ D33
HallC52×C11 ⋊ D3×C23
HallC11×C23 ⋊ C5×D15
HallC3×C52 ⋊ D11×C23
HallC3×C23 ⋊ C5×D55
HallC3×C11 ⋊ C5×D5×C23
SylowC52 ⋊ C23×D33
SylowC11 ⋊ C5×C23×D15
SylowC3 ⋊ C5×C23×D55

Subgroups

subgroupG/H
center, hypercenterC5×C23D165
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C23
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C5×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7590

Conjugacy classes & character table

9660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 97);