Finite Group Databasebeta

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C5×D15×C23⋊C11 #49182111

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

Aliases

direct productC5×D15×C23⋊C11
unambiguous semidirect productC3⋊(C5×D5×C23⋊C11)
unambiguous semidirect productC5⋊(C5×D3×C23⋊C11)
unambiguous semidirect product(C23×D15)⋊(C5×C11)
unambiguous semidirect product(C5×C23×D15)⋊C11

Splittings

Fitting, socle, HallC3×C52×C23 ⋊ C2×C11
derivedC3×C5×C23 ⋊ C2×C5×C11
HallC3×C52×C23⋊C11 ⋊ C2
HallC52×C23⋊C11 ⋊ D3
HallC5×C23×D15 ⋊ C11
HallC3×C23⋊C11 ⋊ C5×D5
HallC52×C23 ⋊ D3×C11
HallC3×C52 ⋊ C2×C23⋊C11
HallC3×C23 ⋊ C5×D5×C11
SylowC52 ⋊ D3×C23⋊C11
SylowC23 ⋊ C5×C11×D15
SylowC3 ⋊ C5×D5×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC5D15×C23⋊C11
commutator, cosocle, hypocenterC3×C5×C23C2×C5×C11
FrattiniC1G
Fitting, socleC3×C52×C23C2×C11
LCSG ▷ C3×C5×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 48);