Finite Group Databasebeta

#546×Dic67 #31015640

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#546×Dic67

Splittings

SylowC67 ⋊ C4×#546

Subgroups

subgroupG/H
center, FrattiniC23C24×D67
commutatorC22×C67C24×C4
Fitting, prime radicalC2×#546×C67C2
socle, cosocleC23×C67C25
hypercenterC2×#546D67
hypocenterC67C4×#546
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#546

3720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 329377);