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C2×C3×C25×D49 #28412855

order14700
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C25×D49

Splittings

FittingC2×C3×C25×C49 ⋊ C2
derived, SylowC49 ⋊ C22×C3×C25
HallC3×C25×C49 ⋊ C22
HallC25×C49 ⋊ C22×C3
HallC3×C49 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D49
commutator, hypocenterC49C22×C3×C25
FrattiniC5×C7C2×C3×C5×D7
FittingC2×C3×C25×C49C2
socleC2×C3×C5×C7C5×D7
prime radicalC2×C3×C5×D49C5
cosocleC5×C49C22×C3×C5
LCSG ▷ C49
UCSC1 ◁ C2×C3×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 34);