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C23×(C5⋊D5)⋊C9 #23780350

order10350
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C5

Aliases

direct productC23×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C9×C23)
unambiguous semidirect product(C23×C5⋊D5)⋊C9

Splittings

derived, SylowC52 ⋊ C2×C9×C23
HallC23×C52⋊C9 ⋊ C2
HallC23×C5⋊D5 ⋊ C9
HallC52×C23 ⋊ C2×C9
HallC52⋊C9 ⋊ C2×C23
HallC5⋊D5 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C23(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C9×C23
FrattiniC3C23×(C5⋊D5)⋊C3
Fitting, socleC3×C52×C23C2×C3
prime radicalC3×C23×C5⋊D5C3
cosocleC3×C52C2×C3×C23
LCSG ▷ C52
UCSC1 ◁ C3×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

690 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#90646⋊C2, ((C5⋊D5)⋊C9)⋊D23, C23×#1043⋊C9, …
maximal normal subgroup ofC23×#90646⋊C2, ((C5⋊D5)⋊C9)⋊D23, C23×#1043⋊C9, …
maximal quotient ofC23×#1039⋊C9, C2×C23×(C5⋊D5)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 24);