Finite Group Databasebeta

Q8×#88045 #15879619

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#88045

Splittings

FittingC42×Q8×C13 ⋊ C2
SylowC13 ⋊ Q8×#104

Subgroups

subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC42×Q8×C13C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenterC42×Q8D13
hypocenterC13Q8×#104
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C42×Q8

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 186268);