Finite Group Databasebeta

← Prev (#49150647) Next (#49150649) →

C7×C25×#6157 #49150648

order37100
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×#6157

Splittings

Fitting, HallC7×C25×C53 ⋊ C4
derived, SylowC53 ⋊ C4×C7×C25
HallC25×C53 ⋊ C4×C7
HallC7×C53 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25#6157
commutator, hypocenterC53C4×C7×C25
FrattiniC5C5×C7×#6157
FittingC7×C25×C53C4
socleC5×C7×C53C4×C5
prime radicalC5×C7×D53C2×C5
cosocleC5×D53C2×C5×C7
LCSG ▷ C53
UCSC1 ◁ C7×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9275

Conjugacy classes & character table

2975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37100, 10);