Finite Group Databasebeta

C2×#27160854 #38744301

order25216
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27160854

Splittings

SylowC197 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D197
commutatorC2×C197C2×C4×C8
FrattiniC2×C8C22×D197
FittingC22×C16×C197C2
socle, prime radicalC23×C197C2×C8
cosocleC2×C8×C197C23
hypercenterC22×C16D197
hypocenterC197C2×#346
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C22×C8 ◁ C22×C16

200 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, 6099);