Finite Group Databasebeta

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C2×C25×D377 #49179397

order37700
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D377
unambiguous semidirect product(C2×C13)⋊(C25×D29)
unambiguous semidirect product(C2×C29)⋊(C25×D13)

Splittings

FittingC2×C13×C25×C29 ⋊ C2
derived, HallC13×C29 ⋊ C22×C25
HallC13×C25×C29 ⋊ C22
HallC25×C29 ⋊ C2×D13
HallC13×C25 ⋊ C2×D29
SylowC29 ⋊ C2×C25×D13
SylowC13 ⋊ C2×C25×D29

Subgroups

subgroupG/H
center, hypercenterC2×C25D377
commutator, hypocenterC13×C29C22×C25
FrattiniC5C2×C5×D377
FittingC2×C13×C25×C29C2
socleC2×C5×C13×C29C2×C5
prime radicalC2×C5×D377C5
cosocleC5×C13×C29C22×C5
LCSG ▷ C13×C29
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18850

Conjugacy classes & character table

9500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37700, 49);