Finite Group Databasebeta

C2×#27160851 #38742455

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

Aliases

direct productC2×#27160851

Splittings

SylowC197 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4#15691335
commutatorC22×C197C2×C42
FrattiniC22×C4C22×D197
FittingC22×M16×C197C2
socleC22×C197#95
prime radicalC24×C197C2×C4
cosocleC22×C4×C197C23
hypercenterC22×M16D197
hypocenterC197C2×#344
LCSG ▷ C22×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

3964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 4253);