Finite Group Databasebeta

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C2×C32×C5×D31 #19150186

order5580
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×D31

Splittings

Fitting, socleC2×C32×C5×C31 ⋊ C2
derived, SylowC31 ⋊ C22×C32×C5
HallC32×C5×C31 ⋊ C22
HallC32×C31 ⋊ C22×C5
HallC5×C31 ⋊ C22×C32

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D31
commutator, hypocenterC31C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C31C2
LCSG ▷ C31
UCSC1 ◁ C2×C32×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×D31⋊C25, C2×C32×C25×D31, C2×C32×C5×D31⋊C5, …
maximal normal subgroup ofC2×C32×D31⋊C25, C2×C32×C25×D31, C2×C32×C5×D31⋊C5, …
maximal quotient ofC2×C32×C25×D31, C32×C5×D5×D31, C2×C32×C52×D31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 175);