Finite Group Databasebeta

#1303×D67 #30746117

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#1303×D67

Splittings

FittingC67×#1303 ⋊ C2
SylowC67 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D67
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC67×#1303C2
socleC22×C67C2×#95
prime radicalC23×D67C22⋊C4
cosocleC2×C42×C67C23
hypercenter#1303D67
hypocenterC67C2×#1303
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59854);