Finite Group Databasebeta

← Prev (#39905939) Next (#39905941) →

C7×C25×#3866 #39905940

order25900
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×#3866

Splittings

Fitting, HallC7×C25×C37 ⋊ C4
derived, SylowC37 ⋊ C4×C7×C25
HallC25×C37 ⋊ C4×C7
HallC7×C37 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25#3866
commutator, hypocenterC37C4×C7×C25
FrattiniC5C5×C7×#3866
FittingC7×C25×C37C4
socleC5×C7×C37C4×C5
prime radicalC5×C7×D37C2×C5
cosocleC5×D37C2×C5×C7
LCSG ▷ C37
UCSC1 ◁ C7×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6475

Conjugacy classes & character table

2275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25900, 10);