Finite Group Databasebeta

C2×#27161557 #38755903

order25216
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#27161557

Splittings

SylowC197 ⋊ C2×#519

Subgroups

subgroupG/H
centerC23C23×D197
commutatorC2×C197C24×C4
FrattiniC22C24×D197
FittingC23×Q8×C197C2
socleC23×C197C24
prime radicalC24×C197C23
cosocleC22×C197C25
hypercenterC23×Q8D197
hypocenterC197C2×#519
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C23 ◁ C23×Q8

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

3988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 17701);