Finite Group Databasebeta

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C7×C25×#1181 #35204409

order20300
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×#1181

Splittings

Fitting, HallC7×C25×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C7×C25
HallC25×C29 ⋊ C4×C7
HallC7×C29 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25#1181
commutator, hypocenterC29C4×C7×C25
FrattiniC5C5×C7×#1181
FittingC7×C25×C29C4
socleC5×C7×C29C4×C5
prime radicalC5×C7×D29C2×C5
cosocleC5×D29C2×C5×C7
LCSG ▷ C29
UCSC1 ◁ C7×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

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(20300, 25);