Finite Group Databasebeta

Q16×#11745659 #28560144

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ16×#11745659

Splittings

FittingC8×Q16×C59 ⋊ C2
SylowC59 ⋊ M16×Q16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC8×Q16×C59C2
socleC22×C59C2×C4×D4
prime radicalC22×D59C4×D4
cosocleC42×C59C24
hypercenterC8×Q16D59
hypocenterC59M16×Q16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 141023);