Finite Group Databasebeta

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C72×Dic3×C25 #28412918

order14700
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C72×C25 · Schur multiplier (H2) = C7

Aliases

direct productC72×Dic3×C25
unambiguous semidirect productC3⋊(C4×C72×C25)

Splittings

derived, SylowC3 ⋊ C4×C72×C25
HallC3×C72×C25 ⋊ C4
HallC3×C72 ⋊ C4×C25
HallC3×C25 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72×C25D3
commutator, hypocenterC3C4×C72×C25
FrattiniC2×C5C5×D3×C72
FittingC2×C3×C72×C25C2
socle, prime radicalC2×C3×C5×C72C2×C5
cosocleC2×C3×C5C2×C5×C72
LCSG ▷ C3
UCSC1 ◁ C2×C72×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 97);