Finite Group Databasebeta

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C7×C11×#1039⋊C3 #37528367

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC7×C11×#1039⋊C3
unambiguous semidirect product#1039⋊(C3×C7×C11)
unambiguous semidirect product(C11×#1039)⋊(C3×C7)

Splittings

derived, SylowC52 ⋊ C3×C4×C7×C11
HallC7×C11×#1039 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC11×#1039 ⋊ C3×C7
HallC11×C52⋊C3 ⋊ C4×C7
HallC7×#1039 ⋊ C3×C11
HallC7×C52⋊C3 ⋊ C4×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
Hall#1039 ⋊ C3×C7×C11
HallC52⋊C3 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11(C5⋊D5)⋊C3
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC2C7×C11×(C5⋊D5)⋊C3
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C7×C11×C52⋊C3C2
cosocleC2×C52C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C2×C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 178);