Finite Group Databasebeta

C22×#20263237 #38751116

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

Aliases

direct productC22×#20263237

Splittings

SylowC197 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D197
commutatorC2×C197C22×C42
FrattiniC2×C4C23×D197
FittingC22×C42×C197C2
socle, prime radicalC24×C197C2×C4
cosocleC2×C4×C197C24
hypercenterC22×C42D197
hypocenterC197C22×#97
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

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, 12914);