Finite Group Databasebeta

#1943×D67 #30859167

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

Aliases

direct product#1943×D67

Splittings

FittingC67×#1943 ⋊ C2
SylowC67 ⋊ C2×#1943

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#1943C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
cosocleC22×C4×C67C24
hypercenter#1943D67
hypocenterC67C2×#1943
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

1142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 172904);