Finite Group Databasebeta

D8×Dic397 #38762605

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic397

Splittings

SylowC397 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D397
commutatorC4×C397C22×C4
FrattiniC2×C4C22×D397
Fitting, prime radicalC2×D8×C397C2
socleC22×C397C2×D4
cosocleC2×C4×C397C23
hypercenterC2×D8D397
hypocenterC397C4×D8
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 632);