Finite Group Databasebeta

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C2×C25×C211⋊C3 #44539523

order31650
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C25×C211⋊C3
unambiguous semidirect product(C2×C25×C211)⋊C3

Splittings

Fitting, HallC2×C25×C211 ⋊ C3
derived, SylowC211 ⋊ C2×C3×C25
HallC25×C211 ⋊ C2×C3
HallC2×C211 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25C211⋊C3
commutator, hypocenterC211C2×C3×C25
FrattiniC5C2×C5×C211⋊C3
FittingC2×C25×C211C3
socleC2×C5×C211C3×C5
prime radicalC2×C5×C211⋊C3C5
cosocleC5×C211C2×C3×C5
LCSG ▷ C211
UCSC1 ◁ C2×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10550

Conjugacy classes & character table

3650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31650, 3);