Finite Group Databasebeta

C2×#27161696 #38756086

order25216
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#27161696

Splittings

SylowC197 ⋊ C2×#542

Subgroups

subgroupG/H
centerC23C23×D197
commutator, cosocleC22×C197C25
FrattiniC22C24×D197
Fitting, prime radicalC2×#121×C197C2
socleC23×C197C24
hypercenterC2×#121D197
hypocenterC197C2×#542
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ C2×#121

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

2788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 17884);