Finite Group Databasebeta

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C3×C47×Dic55 #44526605

order31020
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×Dic55
unambiguous semidirect productC11⋊(C3×Dic5×C47)

Splittings

derived, HallC5×C11 ⋊ C3×C4×C47
HallC3×C5×C11×C47 ⋊ C4
HallC5×C11×C47 ⋊ C3×C4
HallC3×C11×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ Dic11
HallC11×C47 ⋊ C3×Dic5
HallC5×C47 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C4×C47
HallC3×C11 ⋊ Dic5×C47
HallC3×C5 ⋊ Dic11×C47
SylowC11 ⋊ C3×Dic5×C47
SylowC5 ⋊ C3×Dic11×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C47D55
commutator, hypocenterC5×C11C3×C4×C47
FrattiniC2C3×C47×D55
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C5×C11C2×C3×C47
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

8178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 8);