Finite Group Databasebeta

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C3×C11⋊#11761508 #46854259

order34980
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊#11761508
unambiguous semidirect productC11⋊(C3×#11761508)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C4
derived, HallC5×C11×C53 ⋊ C3×C4
HallC3×C11×C53 ⋊ Dic5
HallC3×C5×C53 ⋊ Dic11
HallC11×C53 ⋊ C3×Dic5
HallC5×C53 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ #6157
HallC3×C53 ⋊ Dic55
HallC5×C11 ⋊ C3×#6157
SylowC53 ⋊ C3×Dic55
HallC3×C11 ⋊ #11761508
HallC3×C5 ⋊ C11⋊#6157
SylowC11 ⋊ C3×#11761508
SylowC5 ⋊ C3×C11⋊#6157

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#11761508
commutator, hypocenterC5×C11×C53C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C53C4
prime radicalC3×C5×C11×D53C2
cosocleC5×C11×D53C2×C3
LCSG ▷ C5×C11×C53
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

2319 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34980, 59);