Finite Group Databasebeta

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C25×Dic7×C37 #39905933

order25900
automorphism?
homologyAbelianization (H1) = C4×C25×C37 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic7×C37
unambiguous semidirect productC7⋊(C4×C25×C37)

Splittings

derived, SylowC7 ⋊ C4×C25×C37
HallC7×C25×C37 ⋊ C4
HallC7×C37 ⋊ C4×C25
HallC7×C25 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC2×C25×C37D7
commutator, hypocenterC7C4×C25×C37
FrattiniC2×C5C5×D7×C37
FittingC2×C7×C25×C37C2
socle, prime radicalC2×C5×C7×C37C2×C5
cosocleC2×C5×C7C2×C5×C37
LCSG ▷ C7
UCSC1 ◁ C2×C25×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25900

Conjugacy classes & character table

9250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25900, 3);