Finite Group Databasebeta

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C11⋊C5×Dic141 #44526619

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

Aliases

direct productC11⋊C5×Dic141
unambiguous semidirect productC3⋊(C11⋊C5×Dic47)
unambiguous semidirect productC47⋊(Dic3×C11⋊C5)
unambiguous semidirect product(C11×Dic141)⋊C5

Splittings

derived, HallC3×C11×C47 ⋊ C4×C5
HallC3×C47×C11⋊C5 ⋊ C4
HallC11×Dic141 ⋊ C5
HallC47×C11⋊C5 ⋊ Dic3
HallC11×C47 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic47
HallC3×C47 ⋊ C4×C11⋊C5
SylowC47 ⋊ Dic3×C11⋊C5
HallC3×C11 ⋊ C5×Dic47
SylowC11 ⋊ C5×Dic141
SylowC3 ⋊ C11⋊C5×Dic47

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D141
commutator, hypocenterC3×C11×C47C4×C5
Fitting, socle, cosocleC2×C3×C11×C47C2×C5
prime radicalC2×C3×C47×C11⋊C5C2
LCSG ▷ C3×C11×C47
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6204

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 22);