Finite Group Databasebeta

C2×Q8×C31⋊C8 #16854633

order3968
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×C31⋊C8

Splittings

SylowC31 ⋊ C2×C8×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C23×C8
FrattiniC2×C4C23×D31
FittingC2×C4×Q8×C31C2
socle, prime radicalC23×C31C22×C4
cosocleC2×C4×C31C24
hypercenterC2×C4×Q8D31
hypocenterC31C2×C8×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

440 conjugacy classes of subgroups; only the 333 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 333 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

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, 13432);