Finite Group Databasebeta

C2×C4×#15691335 #38745043

order25216
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#15691335

Splittings

FittingC22×C42×C197 ⋊ C2
SylowC197 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D197
commutatorC2×C197C22×C42
FrattiniC23C23×D197
FittingC22×C42×C197C2
socleC24×C197C23
prime radicalC24×D197C22
cosocleC23×C197C24
hypercenterC22×C42D197
hypocenterC197C2×C4×C22⋊C4
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

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, 6841);