Finite Group Databasebeta

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C3×C49×Dic25 #28412828

order14700
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×Dic25

Splittings

derived, SylowC25 ⋊ C3×C4×C49
HallC3×C25×C49 ⋊ C4
HallC25×C49 ⋊ C3×C4
HallC3×C25 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C49D25
commutator, hypocenterC25C3×C4×C49
FrattiniC2×C5×C7C3×C7×D5
FittingC2×C3×C25×C49C2
socle, prime radicalC2×C3×C5×C7C7×D5
cosocleC2×C7×C25C2×C3×C7
LCSG ▷ C25
UCSC1 ◁ C2×C3×C49

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 7);