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C25×C3⋊(C7⋊Dic7) #28412920

order14700
automorphism?
homologyAbelianization (H1) = C4×C25 · Schur multiplier (H2) = C7

Aliases

direct productC25×C3⋊(C7⋊Dic7)
unambiguous semidirect productC3⋊(C25×C7⋊Dic7)
unambiguous semidirect productC7⋊(C25×Dic21)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C25C3⋊(C7⋊D7)
commutator, hypocenterC3×C72C4×C25
FrattiniC2×C5C5×C3⋊(C7⋊D7)
FittingC2×C3×C72×C25C2
socle, prime radical, cosocleC2×C3×C5×C72C2×C5
LCSG ▷ C3×C72
UCSC1 ◁ C2×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 99);