Finite Group Databasebeta

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C11×C25×#261 #28384649

order14300
isoclinismisoclinic class of #261
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×#261

Splittings

Fitting, HallC11×C13×C25 ⋊ C4
derived, SylowC13 ⋊ C4×C11×C25
HallC13×C25 ⋊ C4×C11
HallC11×C13 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25#261
commutator, hypocenterC13C4×C11×C25
FrattiniC5C5×C11×#261
FittingC11×C13×C25C4
socleC5×C11×C13C4×C5
prime radicalC5×C11×D13C2×C5
cosocleC5×D13C2×C5×C11
LCSG ▷ C13
UCSC1 ◁ C11×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3575

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14300, 21);