Finite Group Databasebeta

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C2×C25⋊(#66526⋊C2) #45685841

order33300
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25⋊(#66526⋊C2)
unambiguous semidirect product(C2×C25)⋊(#66526⋊C2)
unambiguous semidirect product(C2×#66526)⋊D25

Splittings

FittingC2×C25×C37 ⋊ C2×C9
derived, HallC25×C37 ⋊ C22×C9
HallC25×#66526 ⋊ C22
HallC2×D925 ⋊ C9
Hall#66526 ⋊ C2×D25
SylowC37 ⋊ C2×C9×D25
SylowC25 ⋊ C2×#66526⋊C2

Subgroups

subgroupG/H
center, hypercenterC2C25⋊(#66526⋊C2)
commutator, hypocenterC25×C37C22×C9
FrattiniC5C2×C5⋊(#66526⋊C2)
FittingC2×C25×C37C2×C9
socleC2×C5×C37C9×D5
prime radicalC2×C25⋊(D37⋊C3)C3
cosocleC25×C37⋊C3C22×C3
LCSG ▷ C25×C37
UCSC1 ◁ C2

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1850

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 114);