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C5×C7×C3⋊D111 #37552143

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

Aliases

direct productC5×C7×C3⋊D111
unambiguous semidirect productC3⋊(C5×C7×D111)
unambiguous semidirect productC37⋊(C5×C7×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C7×C37 ⋊ C2
derived, HallC32×C37 ⋊ C2×C5×C7
HallC32×C7×C37 ⋊ C2×C5
HallC32×C5×C37 ⋊ C2×C7
HallC5×C7×C37 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D37
HallC7×C37 ⋊ C5×C3⋊D3
HallC5×C37 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ C5×D37
HallC32×C5 ⋊ C7×D37
SylowC37 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C5×C7×D37

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D111
commutator, cosocle, hypocenterC32×C37C2×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C37C2
LCSG ▷ C32×C37
UCSC1 ◁ C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 162);