Finite Group Databasebeta

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C11×C19×Dic25 #35229824

order20900
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC11×C19×Dic25

Splittings

derived, SylowC25 ⋊ C4×C11×C19
HallC11×C19×C25 ⋊ C4
HallC19×C25 ⋊ C4×C11
HallC11×C25 ⋊ C4×C19

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D25
commutator, hypocenterC25C4×C11×C19
FrattiniC2×C5D5×C11×C19
FittingC2×C11×C19×C25C2
socle, prime radicalC2×C5×C11×C19D5
cosocleC2×C25C2×C11×C19
LCSG ▷ C25
UCSC1 ◁ C2×C11×C19

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20900

Conjugacy classes & character table

5852 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 6);