Finite Group Databasebeta

Q16×#11924005 #33101841

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ16×#11924005

Splittings

FittingC2×C4×Q16×C73 ⋊ C2
SylowC73 ⋊ C22⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×Q16×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenterC2×C4×Q16D73
hypocenterC73C22⋊C4×Q16
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2086 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 185425);