Finite Group Databasebeta

Q8×#15691787 #38762648

order25408
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productQ8×#15691787

Splittings

SylowC397 ⋊ C8×Q8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D397
commutatorC2×C397C22×C8
FittingC4×Q8×C397C2
socle, prime radicalC22×C397C22×C4
cosocleC2×C4×C397C23
hypercenterC4×Q8D397
hypocenterC397C8×Q8
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C4×Q8

102 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, 675);