Finite Group Databasebeta

C4×Dic164 #14580432

order2624
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic164

Splittings

SylowC41 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D164
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
FittingC4×C8×C41C2
socle, prime radicalC22×C41C2×D4
cosocleC2×C4×C41C23
hypercenterC4×C8D41
hypocenterC41C4×Q16
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2624

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 645);