Finite Group Databasebeta

← Prev (#28412912) Next (#28412914) →

C3×C7×C25×Dic7 #28412913

order14700
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C25×Dic7

Splittings

derivedC7 ⋊ C3×C4×C7×C25
HallC3×C72×C25 ⋊ C4
HallC72×C25 ⋊ C3×C4
HallC3×C72 ⋊ C4×C25
SylowC72 ⋊ C3×C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C25D7
commutator, hypocenterC7C3×C4×C7×C25
FrattiniC2×C5C3×C5×C7×D7
FittingC2×C3×C72×C25C2
socle, prime radicalC2×C3×C5×C72C2×C5
cosocleC2×C5×C7C2×C3×C5×C7
LCSG ▷ C7
UCSC1 ◁ C2×C3×C7×C25

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 92);