Finite Group Databasebeta

C4×#11758407 #16845613

order3968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#11758407

Splittings

SylowC31 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D124
commutatorC4×C31C2×C42
FrattiniC22×C4C22×D31
FittingC2×C4×C8×C31C2
socleC22×C31C2×C4⋊C4
prime radicalC23×C31C2×Q8
cosocleC22×C4×C31C23
hypercenterC2×C4×C8D31
hypocenterC31C4×#108
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

1016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 4412);