Finite Group Databasebeta

C16×Dic398 #38770753

order25472
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic398

Splittings

SylowC199 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D199
commutatorC2×C199C22×C16
FrattiniC2×C8C22×D199
FittingC4×C16×C199C2
socle, prime radicalC22×C199C22×C8
cosocleC2×C8×C199C23
hypercenterC4×C16D199
hypocenterC199Q8×C16
LCSG ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25472

Conjugacy classes & character table

6416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 6413);