Finite Group Databasebeta

C22×C4×Dic62 #16858886

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×C4×Dic62

Splittings

SylowC31 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC22×C42×C31C2
socle, prime radicalC24×C31C23
cosocleC22×C31C25
hypercenterC22×C42D31
hypocenterC31C22×C4×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C22×C42

1664 conjugacy classes of subgroups; only the 981 normal subgroups are shown.

normal subgroups only

This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 981 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

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17685);