Finite Group Databasebeta

← Prev (#38788144) Next (#38788146) →

C5×C11×#90865 #38788145

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×#90865

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C13 ⋊ C4×C5×C11
HallC32×C11×C13 ⋊ C4×C5
HallC5×C11×C13 ⋊ #157
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C5×#157
HallC32×C11 ⋊ C5×Dic13
HallC5×C13 ⋊ C11×#157
HallC32×C5 ⋊ C11×Dic13
SylowC13 ⋊ C5×C11×#157
SylowC32 ⋊ C5×C11×Dic13

Subgroups

subgroupG/H
center, hypercenterC5×C11#90865
commutator, hypocenterC32×C13C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC5×C11×C13×C3⋊D3C2
cosocleC13×C3⋊D3C2×C5×C11
LCSG ▷ C32×C13
UCSC1 ◁ C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 376);