Finite Group Databasebeta

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C2×C25×D321 #44545626

order32100
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D321
unambiguous semidirect product(C2×C3)⋊(C25×D107)
unambiguous semidirect product(C2×C107)⋊(D3×C25)

Splittings

FittingC2×C3×C25×C107 ⋊ C2
derived, HallC3×C107 ⋊ C22×C25
HallC3×C25×C107 ⋊ C22
HallC25×C107 ⋊ C2×D3
SylowC107 ⋊ C2×D3×C25
HallC3×C25 ⋊ C2×D107
SylowC3 ⋊ C2×C25×D107

Subgroups

subgroupG/H
center, hypercenterC2×C25D321
commutator, hypocenterC3×C107C22×C25
FrattiniC5C2×C5×D321
FittingC2×C3×C25×C107C2
socleC2×C3×C5×C107C2×C5
prime radicalC2×C5×D321C5
cosocleC3×C5×C107C22×C5
LCSG ▷ C3×C107
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16050

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 24);