Finite Group Databasebeta

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C3×C5×D5×C11×C23 #49182146

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D5×C11×C23
unambiguous semidirect productC5⋊(C2×C3×C5×C11×C23)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derivedC5 ⋊ C2×C3×C5×C11×C23
HallC52×C11×C23 ⋊ C2×C3
HallC3×C52×C23 ⋊ C2×C11
HallC3×C52×C11 ⋊ C2×C23
HallC52×C23 ⋊ C2×C3×C11
HallC52×C11 ⋊ C2×C3×C23
HallC3×C52 ⋊ C2×C11×C23
SylowC52 ⋊ C2×C3×C11×C23

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11×C23D5
commutator, cosocle, hypocenterC5C2×C3×C5×C11×C23
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C5
UCSC1 ◁ C3×C5×C11×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7590

Conjugacy classes & character table

15180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 83);