Finite Group Databasebeta

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C7×C37×Dic25 #39905935

order25900
automorphism?
homologyAbelianization (H1) = C4×C7×C37 · Schur multiplier (H2) = C1

Aliases

direct productC7×C37×Dic25

Splittings

derived, SylowC25 ⋊ C4×C7×C37
HallC7×C25×C37 ⋊ C4
HallC25×C37 ⋊ C4×C7
HallC7×C25 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC2×C7×C37D25
commutator, hypocenterC25C4×C7×C37
FrattiniC2×C5C7×D5×C37
FittingC2×C7×C25×C37C2
socle, prime radicalC2×C5×C7×C37D5
cosocleC2×C25C2×C7×C37
LCSG ▷ C25
UCSC1 ◁ C2×C7×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25900

Conjugacy classes & character table

7252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25900, 5);