Finite Group Databasebeta

C2×Q8×Dic397 #38762988

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

Aliases

direct productC2×Q8×Dic397

Splittings

SylowC397 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D397
commutatorC2×C397C23×C4
FrattiniC22C23×D397
FittingC22×Q8×C397C2
socle, prime radicalC23×C397C23
cosocleC22×C397C24
hypercenterC22×Q8D397
hypocenterC397C2×C4×Q8
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1015);