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C72×(C5⋊D5)⋊C3 #20301287

order7350
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C5×C7

Aliases

direct productC72×(C5⋊D5)⋊C3
unambiguous semidirect product(C5⋊D5)⋊(C3×C72)

Splittings

Fitting, socle, HallC52×C72 ⋊ C2×C3
derived, SylowC52 ⋊ C2×C3×C72
HallC72×C52⋊C3 ⋊ C2
HallC72×C5⋊D5 ⋊ C3
HallC52⋊C3 ⋊ C2×C72
HallC5⋊D5 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC72(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C3×C72
FrattiniC1G
Fitting, socleC52×C72C2×C3
LCSG ▷ C52
UCSC1 ◁ C72

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC72×#3874⋊C2, C7×((C5⋊D5)⋊C3)⋊D7, ((C5⋊D5)⋊C3)⋊(C7⋊D7), …
maximal normal subgroup ofC72×#3874⋊C2, C7×((C5⋊D5)⋊C3)⋊D7, ((C5⋊D5)⋊C3)⋊(C7⋊D7), …
maximal quotient ofC72×#1039⋊C3, C2×C72×(C5⋊D5)⋊C3, C72×(C5⋊D5)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 110);