Finite Group Databasebeta

Q16×C4⋊Dic67 #30874263

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ16×C4⋊Dic67

Splittings

SylowC67 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×C4×Q16×C67C2
socle, prime radicalC23×C67C22×D4
cosocleC22×C4×C67C24
hypercenterC2×C4×Q16D67
hypocenterC67C4⋊C4×Q16
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1918 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 188000);