Finite Group Databasebeta

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C2×C3×C7×C11×C5⋊D5 #37528744

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C7×C11×C5⋊D5
unambiguous semidirect product(C2×C5)⋊(C3×C7×D5×C11)

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, SylowC52 ⋊ C22×C3×C7×C11
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C22×C7
HallC3×C52×C7 ⋊ C22×C11
HallC52×C11 ⋊ C22×C3×C7
HallC52×C7 ⋊ C22×C3×C11
HallC3×C52 ⋊ C22×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C11C5⋊D5
commutator, cosocle, hypocenterC52C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C52
UCSC1 ◁ C2×C3×C7×C11

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 555);