Finite Group Databasebeta

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C2×C3×C7×D11×C25 #37528313

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D11×C25

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, SylowC11 ⋊ C22×C3×C7×C25
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C22×C3
HallC3×C11×C25 ⋊ C22×C7
HallC11×C25 ⋊ C22×C3×C7
HallC3×C7×C11 ⋊ C22×C25
HallC7×C11 ⋊ C22×C3×C25
HallC3×C11 ⋊ C22×C7×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C25D11
commutator, hypocenterC11C22×C3×C7×C25
FrattiniC5C2×C3×C5×C7×D11
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×D11C5
cosocleC5×C11C22×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C3×C7×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 124);