Finite Group Databasebeta

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C3×C7×C11×D55 #38763780

order25410
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D55
unambiguous semidirect productC5⋊(C3×C7×C11×D11)
unambiguous semidirect productC11⋊(C3×C7×D5×C11)

Splittings

Fitting, socle, HallC3×C5×C7×C112 ⋊ C2
derivedC5×C11 ⋊ C2×C3×C7×C11
HallC5×C7×C112 ⋊ C2×C3
HallC3×C7×C112 ⋊ D5
HallC3×C5×C112 ⋊ C2×C7
HallC7×C112 ⋊ C3×D5
HallC5×C112 ⋊ C2×C3×C7
HallC3×C112 ⋊ C7×D5
SylowC112 ⋊ C3×C7×D5
HallC3×C5×C7 ⋊ C11×D11
HallC5×C7 ⋊ C3×C11×D11
HallC3×C5 ⋊ C7×C11×D11
SylowC5 ⋊ C3×C7×C11×D11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D55
commutator, cosocle, hypocenterC5×C11C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C112C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C7×C11

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

6699 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25410, 176);