Finite Group Databasebeta

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C11×Dic705 #44526612

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

Aliases

direct productC11×Dic705
unambiguous semidirect productC3⋊(C11×Dic235)
unambiguous semidirect productC47⋊(C11×Dic15)

Splittings

derived, HallC3×C5×C47 ⋊ C4×C11
HallC3×C5×C11×C47 ⋊ C4
HallC5×C11×C47 ⋊ Dic3
HallC3×C11×C47 ⋊ Dic5
HallC11×C47 ⋊ Dic15
HallC5×C47 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic47
HallC3×C47 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic141
SylowC47 ⋊ C11×Dic15
HallC3×C11 ⋊ Dic235
HallC3×C5 ⋊ C11×Dic47
SylowC5 ⋊ C11×Dic141
SylowC3 ⋊ C11×Dic235

Subgroups

subgroupG/H
center, hypercenterC2×C11D705
commutator, hypocenterC3×C5×C47C4×C11
FrattiniC2C11×D705
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C3×C5×C47C2×C11
LCSG ▷ C3×C5×C47
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

7788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 15);