Finite Group Databasebeta

C16×Dic394 #38744615

order25216
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic394

Splittings

SylowC197 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D197
commutatorC2×C197C22×C16
FrattiniC2×C8C22×D197
FittingC4×C16×C197C2
socle, prime radicalC22×C197C22×C8
cosocleC2×C8×C197C23
hypercenterC4×C16D197
hypocenterC197Q8×C16
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

6352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 6413);