Finite Group Databasebeta

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C13×C25×#1181 #49179358

order37700
automorphism?
homologyAbelianization (H1) = C4×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25×#1181

Splittings

Fitting, HallC13×C25×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C13×C25
HallC25×C29 ⋊ C4×C13
HallC13×C29 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC13×C25#1181
commutator, hypocenterC29C4×C13×C25
FrattiniC5C5×C13×#1181
FittingC13×C25×C29C4
socleC5×C13×C29C4×C5
prime radicalC5×C13×D29C2×C5
cosocleC5×D29C2×C5×C13
LCSG ▷ C29
UCSC1 ◁ C13×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9425

Conjugacy classes & character table

3575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37700, 10);