Finite Group Databasebeta

C2×C4×C8×D31 #16854110

order3968
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D31

Splittings

FittingC2×C4×C8×C31 ⋊ C2
derived, SylowC31 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D31
commutator, hypocenterC31C22×C4×C8
FrattiniC2×C4C23×D31
FittingC2×C4×C8×C31C2
socleC23×C31C22×C4
prime radicalC23×D31C2×C4
cosocleC2×C4×C31C24
LCSG ▷ C31
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 12909);