Finite Group Databasebeta

C2×C22⋊C8×D31 #16854141

order3968
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D31

Splittings

FittingC2×C31×C22⋊C8 ⋊ C2
SylowC31 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C23×C8
FrattiniC2×C4C23×D31
FittingC2×C31×C22⋊C8C2
socleC23×C31C22×C4
prime radicalC24×D31C4
cosocleC2×C4×C31C24
hypercenterC2×C22⋊C8D31
hypocenterC31C22×C22⋊C8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 12940);