Finite Group Databasebeta

#376×Dic67 #30776902

order17152
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C44

Aliases

direct product#376×Dic67

Splittings

SylowC67 ⋊ C4×#376

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C2×C43
FrattiniC24C23×D67
FittingC2×#376×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC2×#376D67
hypocenterC67C4×#376
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×#376

2302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 90639);