Finite Group Databasebeta

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C7×C11×C3⋊#1039 #37528388

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

Aliases

direct productC7×C11×C3⋊#1039
unambiguous semidirect productC3⋊(C7×C11×#1039)

Splittings

derived, HallC3×C52 ⋊ C4×C7×C11
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1039
HallC52×C7 ⋊ C11×Dic3
HallC3×C11 ⋊ C7×#1039
SylowC52 ⋊ C7×C11×Dic3
HallC3×C7 ⋊ C11×#1039
SylowC3 ⋊ C7×C11×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C4×C7×C11
FrattiniC2C7×C11×C3⋊(C5⋊D5)
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C3×C52C2×C7×C11
LCSG ▷ C3×C52
UCSC1 ◁ C2×C7×C11

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 199);