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C4×C72×C52⋊C3 #28413191

order14700
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C5×C7

Aliases

direct productC4×C72×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C72)

Splittings

Fitting, HallC4×C52×C72 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C72
HallC52×C72 ⋊ C3×C4
HallC4×C52 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC4×C72C52⋊C3
commutator, hypocenterC52C3×C4×C72
FrattiniC2C2×C72×C52⋊C3
FittingC4×C52×C72C3
socleC2×C52×C72C2×C3
prime radicalC2×C72×C52⋊C3C2
cosocleC2×C52C2×C3×C72
LCSG ▷ C52
UCSC1 ◁ C4×C72

180 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, 370);