Finite Group Databasebeta

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C2×D25×C361 #49115449

order36100
automorphism?
homologyAbelianization (H1) = C22×C361 · Schur multiplier (H2) = C2

Aliases

direct productC2×D25×C361
unambiguous semidirect productC25⋊(C22×C361)
unambiguous semidirect product(C2×C25)⋊(C2×C361)

Splittings

FittingC2×C25×C361 ⋊ C2
derived, SylowC25 ⋊ C22×C361
HallC25×C361 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C361D25
commutator, hypocenterC25C22×C361
FrattiniC5×C19C2×D5×C19
FittingC2×C25×C361C2
socleC2×C5×C19D5×C19
prime radicalC2×C19×D25C19
cosocleC19×C25C22×C19
LCSG ▷ C25
UCSC1 ◁ C2×C361

45 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18050

Conjugacy classes & character table

10108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36100, 10);