Finite Group Databasebeta

← Prev (#37528506) Next (#37528508) →

C7×C11×#1043⋊C3 #37528507

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×#1043⋊C3
unambiguous semidirect product#1043⋊(C3×C7×C11)
unambiguous semidirect product(C11×#1043)⋊(C3×C7)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C3×C4
derived, SylowC52 ⋊ C3×C4×C7×C11
HallC7×C11×#1043 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C4
HallC11×#1043 ⋊ C3×C7
HallC11×C52⋊C3 ⋊ C4×C7
HallC7×#1043 ⋊ C3×C11
HallC7×C52⋊C3 ⋊ C4×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
Hall#1043 ⋊ C3×C7×C11
HallC52⋊C3 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11#1043⋊C3
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC1G
Fitting, socleC52×C7×C11C3×C4
prime radicalC7×C11×(C5⋊D5)⋊C3C2
cosocleC5⋊D5C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 318);