Finite Group Databasebeta

Q8×#14519689 #29696526

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#14519689

Splittings

FittingC2×C8×Q8×C61 ⋊ C2
SylowC61 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC2×C8×Q8×C61C2
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC2×C8×Q8D61
hypocenterC61Q8×C22⋊C8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 186081);