Finite Group Databasebeta

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C2×C25×D231 #37528323

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

Aliases

direct productC2×C25×D231
unambiguous semidirect product(C2×C3)⋊(C25×D77)
unambiguous semidirect product(C2×C7)⋊(C25×D33)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC3×C7×C11 ⋊ C22×C25
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D21
HallC7×C25 ⋊ C2×D33
HallC7×C11 ⋊ C2×D3×C25
HallC3×C25 ⋊ C2×D77
HallC3×C11 ⋊ C2×D7×C25
HallC3×C7 ⋊ C2×D11×C25
SylowC11 ⋊ C2×C25×D21
SylowC7 ⋊ C2×C25×D33
SylowC3 ⋊ C2×C25×D77

Subgroups

subgroupG/H
center, hypercenterC2×C25D231
commutator, hypocenterC3×C7×C11C22×C25
FrattiniC5C2×C5×D231
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C5×D231C5
cosocleC3×C5×C7×C11C22×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 134);