Finite Group Databasebeta

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C3×C5×Dic517 #44526602

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

Aliases

direct productC3×C5×Dic517
unambiguous semidirect productC47⋊(C3×C5×Dic11)

Splittings

derived, HallC11×C47 ⋊ C3×C4×C5
HallC3×C5×C11×C47 ⋊ C4
HallC5×C11×C47 ⋊ C3×C4
HallC3×C11×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ Dic11
HallC5×C47 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic47
HallC3×C47 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×Dic47
SylowC47 ⋊ C3×C5×Dic11
HallC3×C11 ⋊ C5×Dic47
SylowC11 ⋊ C3×C5×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D517
commutator, hypocenterC11×C47C3×C4×C5
FrattiniC2C3×C5×D517
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C11×C47C2×C3×C5
LCSG ▷ C11×C47
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

7800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 5);