Finite Group Databasebeta

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C7×C11⋊(#1039⋊C3) #37528368

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

Aliases

direct productC7×C11⋊(#1039⋊C3)
unambiguous semidirect productC11⋊(C7×#1039⋊C3)
unambiguous semidirect product(C11⋊#1039)⋊(C3×C7)

Splittings

derived, HallC52×C11 ⋊ C3×C4×C7
HallC7×C11⋊#1039 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC11⋊#1039 ⋊ C3×C7
HallC11×C52⋊C3 ⋊ C4×C7
HallC7×C52⋊C3 ⋊ Dic11
HallC52×C7 ⋊ C3×Dic11
HallC7×C11 ⋊ #1039⋊C3
HallC52⋊C3 ⋊ C7×Dic11
SylowC52 ⋊ C3×C7×Dic11
SylowC11 ⋊ C7×#1039⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C11⋊((C5⋊D5)⋊C3)
commutator, hypocenterC52×C11C3×C4×C7
FrattiniC2C7×C11⋊((C5⋊D5)⋊C3)
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C7×C11×C52⋊C3C2
cosocleC2×C52×C11C2×C3×C7
LCSG ▷ C52×C11
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 179);