Finite Group Databasebeta

C2×C8×Dic332 #35373776

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×Dic332

Splittings

SylowC83 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC22×C8D332
commutatorC4×C83C23×C8
FrattiniC42C23×D83
FittingC2×C82×C83C2
socle, prime radicalC23×C83C4×D4
cosocleC42×C83C24
hypercenterC2×C82D83
hypocenterC83C2×C8×Q16
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

5360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 138940);