Finite Group Databasebeta

C2×#27161208 #38751638

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27161208

Splittings

SylowC197 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D197
commutatorC22×C197C23×C4
FrattiniC2×C4C23×D197
FittingC2×C4⋊C8×C197C2
socle, prime radicalC23×C197C22×C4
cosocleC2×C4×C197C24
hypercenterC2×C4⋊C8D197
hypocenterC197C2×#446
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

3976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13436);