Finite Group Databasebeta

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C2×C32×C5×D91 #30655799

order16380
isoclinismisoclinic class of D91
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×D91

Splittings

Fitting, socleC2×C32×C5×C7×C13 ⋊ C2
derived, HallC7×C13 ⋊ C22×C32×C5
HallC32×C5×C7×C13 ⋊ C22
HallC32×C7×C13 ⋊ C22×C5
HallC32×C5×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C22×C32
HallC32×C5×C7 ⋊ C2×D13
HallC32×C13 ⋊ C2×C5×D7
HallC5×C13 ⋊ C2×C32×D7
HallC32×C7 ⋊ C2×C5×D13
HallC5×C7 ⋊ C2×C32×D13
SylowC13 ⋊ C2×C32×C5×D7
SylowC7 ⋊ C2×C32×C5×D13

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D91
commutator, cosocle, hypocenterC7×C13C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C32×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

4230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 849);