Finite Group Databasebeta

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C5×C19×C11⋊#157 #49178647

order37620
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC5×C19×C11⋊#157

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derived, HallC32×C11 ⋊ C4×C5×C19
HallC32×C11×C19 ⋊ C4×C5
HallC5×C11×C19 ⋊ #157
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ C4×C19
HallC11×C19 ⋊ C5×#157
HallC32×C19 ⋊ C5×Dic11
HallC5×C11 ⋊ C19×#157
HallC32×C5 ⋊ C19×Dic11
SylowC11 ⋊ C5×C19×#157
SylowC32 ⋊ C5×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC5×C19C11⋊#157
commutator, hypocenterC32×C11C4×C5×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC5×C11×C3⋊D3×C19C2
cosocleC11×C3⋊D3C2×C5×C19
LCSG ▷ C32×C11
UCSC1 ◁ C5×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 356);