Finite Group Databasebeta

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C11×C25×#595 #34035136

order18700
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×#595

Splittings

Fitting, HallC11×C17×C25 ⋊ C4
derived, SylowC17 ⋊ C4×C11×C25
HallC17×C25 ⋊ C4×C11
HallC11×C17 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25#595
commutator, hypocenterC17C4×C11×C25
FrattiniC5C5×C11×#595
FittingC11×C17×C25C4
socleC5×C11×C17C4×C5
prime radicalC5×C11×D17C2×C5
cosocleC5×D17C2×C5×C11
LCSG ▷ C17
UCSC1 ◁ C11×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4675

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 21);