Finite Group Databasebeta

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C3×C5×D3×C7×C37 #37552134

order23310
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D3×C7×C37
unambiguous semidirect productC3⋊(C2×C3×C5×C7×C37)

Splittings

Fitting, socle, HallC32×C5×C7×C37 ⋊ C2
derivedC3 ⋊ C2×C3×C5×C7×C37
HallC32×C7×C37 ⋊ C2×C5
HallC32×C5×C37 ⋊ C2×C7
HallC32×C37 ⋊ C2×C5×C7
HallC32×C5×C7 ⋊ C2×C37
HallC32×C7 ⋊ C2×C5×C37
HallC32×C5 ⋊ C2×C7×C37
SylowC32 ⋊ C2×C5×C7×C37

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C37D3
commutator, cosocle, hypocenterC3C2×C3×C5×C7×C37
FrattiniC1G
Fitting, socleC32×C5×C7×C37C2
LCSG ▷ C3
UCSC1 ◁ C3×C5×C7×C37

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7770

Conjugacy classes & character table

11655 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 153);