Finite Group Databasebeta

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C7×C25×Dic37 #39905932

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

Aliases

direct productC7×C25×Dic37

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25D37
commutator, hypocenterC37C4×C7×C25
FrattiniC2×C5C5×C7×D37
FittingC2×C7×C25×C37C2
socle, prime radicalC2×C5×C7×C37C2×C5
cosocleC2×C5×C37C2×C5×C7
LCSG ▷ C37
UCSC1 ◁ C2×C7×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25900

Conjugacy classes & character table

7000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25900, 2);