Finite Group Databasebeta

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C22×C3×C5×C7×C11⋊C5 #37528598

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C52×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C3×C5×C7×C11⋊C5
unambiguous semidirect product(C22×C3×C11)⋊(C52×C7)
unambiguous semidirect product(C22×C3×C5×C11)⋊(C5×C7)
unambiguous semidirect product(C22×C3×C7×C11)⋊C52
unambiguous semidirect product(C22×C3×C5×C7×C11)⋊C5

Splittings

Fitting, socleC22×C3×C5×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C52×C7
HallC22×C3×C7×C11 ⋊ C52
HallC22×C7×C11 ⋊ C3×C52
HallC3×C7×C11 ⋊ C22×C52
HallC22×C3×C11 ⋊ C52×C7
HallC7×C11 ⋊ C22×C3×C52
HallC22×C11 ⋊ C3×C52×C7
HallC3×C11 ⋊ C22×C52×C7

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5×C7C11⋊C5
commutator, cosocle, hypocenterC11C22×C3×C52×C7
FrattiniC1G
Fitting, socleC22×C3×C5×C7×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C3×C5×C7

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 409);