Finite Group Databasebeta

M16×#11761617 #30827273

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#11761617

Splittings

FittingC8×M16×C67 ⋊ C2
SylowC67 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×D268
commutatorC2×C4×C67C23×C4
FrattiniC42C23×D67
FittingC8×M16×C67C2
socleC22×C67C2×C4×D4
prime radicalC22×D268C2×C4
cosocleC42×C67C24
hypercenterC8×M16D67
hypocenterC67M16×SD16
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 141010);