Finite Group Databasebeta

← Prev (#28412876) Next (#28412878) →

C4×C49×C52⋊C3 #28412877

order14700
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C5

Aliases

direct productC4×C49×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C49)

Splittings

Fitting, HallC4×C52×C49 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C49
HallC52×C49 ⋊ C3×C4
HallC4×C52 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC4×C49C52⋊C3
commutator, hypocenterC52C3×C4×C49
FrattiniC2×C7C2×C7×C52⋊C3
FittingC4×C52×C49C3
socle, cosocleC2×C52×C7C2×C3×C7
prime radicalC2×C7×C52⋊C3C2×C7
LCSG ▷ C52
UCSC1 ◁ C4×C49

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 56);