Finite Group Databasebeta

C22×#20263741 #38763596

order25408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#20263741

Splittings

SylowC397 ⋊ C22×M16

Subgroups

subgroupG/H
centerC23C2×#13097544
commutatorC2×C397C23×C4
FrattiniC2C23×#13097544
FittingC22×C4×C397C4
socleC23×C397C2×C4
prime radicalC23×D397C4
cosocleDic397C24
hypercenterC22×C4#13097544
hypocenterC397C22×M16
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1623);