Finite Group Databasebeta

← Prev (#38788158) Next (#38788160) →

C11×#14556847 #38788159

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

Aliases

direct productC11×#14556847

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C5×C13 ⋊ C4×C11
HallC32×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ #157
HallC32×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ #4379
HallC32×C13 ⋊ C11×Dic5
HallC32×C11 ⋊ Dic65
HallC5×C13 ⋊ C11×#157
HallC5×C11 ⋊ #90865
HallC32×C5 ⋊ C11×Dic13
SylowC13 ⋊ C11×#4379
SylowC32 ⋊ C11×Dic65
SylowC5 ⋊ C11×#90865

Subgroups

subgroupG/H
center, hypercenterC11#14556847
commutator, hypocenterC32×C5×C13C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC5×C11×C13×C3⋊D3C2
cosocleC5×C13×C3⋊D3C2×C11
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 390);