Finite Group Databasebeta

Q8×#13182029 #28376613

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#13182029

Splittings

FittingC2×C4×Q8×C109 ⋊ C2
SylowC109 ⋊ Q8×#41

Subgroups

subgroupG/H
centerC2×C4C23×D109
commutator, socle, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×C4×Q8×C109C2
prime radicalC2×#13182029C22
hypercenterC2×C4×Q8D109
hypocenterC109Q8×#41
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 18091);