Finite Group Databasebeta

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C7×C25×Dic21 #28412919

order14700
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×Dic21
unambiguous semidirect productC3⋊(C7×C25×Dic7)
unambiguous semidirect productC7⋊(C7×Dic3×C25)

Splittings

derivedC3×C7 ⋊ C4×C7×C25
HallC3×C72×C25 ⋊ C4
HallC72×C25 ⋊ Dic3
HallC3×C72 ⋊ C4×C25
HallC3×C25 ⋊ C7×Dic7
SylowC72 ⋊ Dic3×C25
SylowC3 ⋊ C7×C25×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25D21
commutator, hypocenterC3×C7C4×C7×C25
FrattiniC2×C5C5×C7×D21
FittingC2×C3×C72×C25C2
socle, prime radicalC2×C3×C5×C72C2×C5
cosocleC2×C3×C5×C7C2×C5×C7
LCSG ▷ C3×C7
UCSC1 ◁ C2×C7×C25

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 98);