Finite Group Databasebeta

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C3×C5×C11×Dic47 #44526600

order31020
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×Dic47
unambiguous semidirect productC47⋊(C3×C4×C5×C11)

Splittings

derived, SylowC47 ⋊ C3×C4×C5×C11
HallC3×C5×C11×C47 ⋊ C4
HallC5×C11×C47 ⋊ C3×C4
HallC3×C11×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ C4×C11
HallC11×C47 ⋊ C3×C4×C5
HallC5×C47 ⋊ C3×C4×C11
HallC3×C47 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D47
commutator, hypocenterC47C3×C4×C5×C11
FrattiniC2C3×C5×C11×D47
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C47C2×C3×C5×C11
LCSG ▷ C47
UCSC1 ◁ C2×C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 3);