Finite Group Databasebeta

C2×#27160839 #38742418

order25216
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27160839

Splittings

SylowC197 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4D788
commutatorC4×C197C2×C42
FrattiniC22×C4C22×D197
FittingC22×C42×C197C2
socleC23×C197C22⋊C4
prime radicalC24×C197D4
cosocleC22×C4×C197C23
hypercenterC22×C42D197
hypocenterC197C2×#339
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

6328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 4216);