Finite Group Databasebeta

Q16×#11758189 #29651468

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ16×#11758189

Splittings

FittingC8×Q16×C61 ⋊ C2
SylowC61 ⋊ M16×Q16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×Q16×C61C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenterC8×Q16D61
hypocenterC61M16×Q16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 141023);