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C5×C3⋊#10624382 #24925833

order10860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#10624382
unambiguous semidirect productC3⋊(C5×#10624382)

Splittings

Fitting, socle, HallC3×C5×C181 ⋊ C4
derived, HallC3×C181 ⋊ C4×C5
HallC5×C181 ⋊ Dic3
SylowC181 ⋊ C5×Dic3
HallC3×C5 ⋊ #10624382
SylowC3 ⋊ C5×#10624382

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#10624382
commutator, hypocenterC3×C181C4×C5
FrattiniC1G
Fitting, socleC3×C5×C181C4
prime radicalC3×C5×D181C2
cosocleC3×D181C2×C5
LCSG ▷ C3×C181
UCSC1 ◁ C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊#10624382, C5×C3⋊(#10624382⋊C3), C3×C5×C3⋊#10624382, …
maximal normal subgroup ofC5×C3⋊(#10624382⋊C3), C3×C5×C3⋊#10624382
maximal quotient ofC5×C9⋊#10624382, C3×C5×C3⋊#10624382, C5×C3⋊(C3⋊#10624382)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 49);