Finite Group Databasebeta

← Prev (#37528270) Next (#37528272) →

C3×C7⋊(C11⋊#1035) #37528271

order23100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(C11⋊#1035)
unambiguous semidirect productC11⋊(C3×C7⋊#1035)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C4
derived, HallC7×C11×C25 ⋊ C3×C4
HallC3×C11×C25 ⋊ Dic7
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ #1035
HallC7×C25 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#1035
HallC3×C25 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#1035
SylowC25 ⋊ C3×Dic77
HallC3×C7 ⋊ C11⋊#1035
SylowC11 ⋊ C3×C7⋊#1035
SylowC7 ⋊ C3×C11⋊#1035

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C11⋊#1035)
commutator, hypocenterC7×C11×C25C3×C4
FrattiniC5C3×C7⋊(C11⋊AGL(1,𝔽5))
FittingC3×C7×C11×C25C4
socleC3×C5×C7×C11AGL(1,𝔽5)
prime radicalC3×C7×C11×D25C2
cosocleC7×C11×D25C2×C3
LCSG ▷ C7×C11×C25
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1626 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 82);