Finite Group Databasebeta

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C3×C5×C11×D107 #47977216

order35310
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D107
unambiguous semidirect productC107⋊(C2×C3×C5×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C107 ⋊ C2
derived, SylowC107 ⋊ C2×C3×C5×C11
HallC5×C11×C107 ⋊ C2×C3
HallC3×C11×C107 ⋊ C2×C5
HallC3×C5×C107 ⋊ C2×C11
HallC11×C107 ⋊ C2×C3×C5
HallC5×C107 ⋊ C2×C3×C11
HallC3×C107 ⋊ C2×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D107
commutator, cosocle, hypocenterC107C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C107C2
LCSG ▷ C107
UCSC1 ◁ C3×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17655

Conjugacy classes & character table

9075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35310, 3);