Finite Group Databasebeta

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C2×C3×C5×D93 #19150182

order5580
isoclinismisoclinic class of D93
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D93
unambiguous semidirect product(C2×C3)⋊(C3×C5×D31)

Splittings

Fitting, socleC2×C32×C5×C31 ⋊ C2
derivedC3×C31 ⋊ C22×C3×C5
HallC32×C5×C31 ⋊ C22
HallC32×C31 ⋊ C22×C5
HallC5×C31 ⋊ C2×C3×D3
HallC32×C5 ⋊ C2×D31
SylowC31 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×C5×D31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D93
commutator, hypocenterC3×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1440 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C3⋊(D31⋊C25), C2×C3×C25×D93, C2×C3×C5×C3⋊(D31⋊C5), …
maximal normal subgroup ofC2×C3×C3⋊(D31⋊C25), C2×C3×C25×D93, C2×C3×C5×C3⋊(D31⋊C5), …
maximal quotient ofC2×C3×C25×D93, C3×C5×D5×D93, C2×C3×C52×D93, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 171);