Finite Group Databasebeta

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C3×C5×C23×D55 #49182148

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

Aliases

direct productC3×C5×C23×D55
unambiguous semidirect productC5⋊(C3×C5×D11×C23)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derivedC5×C11 ⋊ C2×C3×C5×C23
HallC52×C11×C23 ⋊ C2×C3
HallC3×C52×C23 ⋊ D11
HallC3×C52×C11 ⋊ C2×C23
HallC3×C11×C23 ⋊ C5×D5
HallC52×C23 ⋊ C3×D11
HallC52×C11 ⋊ C2×C3×C23
HallC11×C23 ⋊ C3×C5×D5
HallC3×C52 ⋊ D11×C23
HallC3×C11 ⋊ C5×D5×C23
SylowC52 ⋊ C3×D11×C23
SylowC11 ⋊ C3×C5×D5×C23

Subgroups

subgroupG/H
center, hypercenterC3×C5×C23D55
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C23
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C5×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7590

Conjugacy classes & character table

10005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 85);