Finite Group Databasebeta

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C2×C11×C25×D21 #37528322

order23100
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C25×D21
unambiguous semidirect product(C2×C3)⋊(C11×D7×C25)
unambiguous semidirect product(C2×C7)⋊(D3×C11×C25)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC3×C7 ⋊ C22×C11×C25
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C25
HallC7×C25 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D3×C25
HallC3×C25 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×D7×C25
SylowC7 ⋊ C2×D3×C11×C25
SylowC3 ⋊ C2×C11×D7×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D21
commutator, hypocenterC3×C7C22×C11×C25
FrattiniC5C2×C5×C11×D21
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C5×C11×D21C5
cosocleC3×C5×C7C22×C5×C11
LCSG ▷ C3×C7
UCSC1 ◁ C2×C11×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

6600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 133);