Finite Group Databasebeta

C22×C4×C22⋊D31 #16858880

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4×C22⋊D31

Splittings

FittingC24×C4×C31 ⋊ C2
SylowC31 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC24×C4×C31C2
socleC24×C31C23
prime radicalC23×C22⋊D31C2
cosocleC22×C31C25
hypercenterC24×C4D31
hypocenterC31C22×C4×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C24×C4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 17679);