Finite Group Databasebeta

C22×#20263258 #38751284

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20263258

Splittings

SylowC197 ⋊ C22×#106

Subgroups

subgroupG/H
centerC24D788
commutatorC4×C197C23×C4
FrattiniC2×C4C23×D197
FittingC23×C8×C197C2
socle, prime radicalC24×C197D4
cosocleC2×C4×C197C24
hypercenterC23×C8D197
hypocenterC197C22×#106
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

6328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13082);