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C72×#1039⋊C3 #28413166

order14700
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C5×C7

Aliases

direct productC72×#1039⋊C3
unambiguous semidirect product#1039⋊(C3×C72)

Splittings

derived, SylowC52 ⋊ C3×C4×C72
HallC72×#1039 ⋊ C3
HallC72×C52⋊C3 ⋊ C4
HallC52×C72 ⋊ C3×C4
Hall#1039 ⋊ C3×C72
HallC52⋊C3 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72(C5⋊D5)⋊C3
commutator, hypocenterC52C3×C4×C72
FrattiniC2C72×(C5⋊D5)⋊C3
Fitting, socleC2×C52×C72C2×C3
prime radicalC2×C72×C52⋊C3C2
cosocleC2×C52C2×C3×C72
LCSG ▷ C52
UCSC1 ◁ C2×C72

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 345);