Finite Group Databasebeta

#1857×D67 #30856637

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#1857×D67

Splittings

FittingC67×#1857 ⋊ C2
SylowC67 ⋊ C2×#1857

Subgroups

subgroupG/H
centerC22#120×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#1857C2
socleC22×C67C2×#120
prime radicalC23×D67C2×D4
cosocleC22×C4×C67C24
hypercenter#1857D67
hypocenterC67C2×#1857
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1857

1402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 170374);