Finite Group Databasebeta

#1294×D67 #30745813

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct product#1294×D67

Splittings

FittingC67×#1294 ⋊ C2
SylowC67 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC23C22⋊C4×D67
commutatorC2×C4×C67C2×C42
FrattiniC23×C4C22×D67
FittingC67×#1294C2
socleC23×C67C2×C22⋊C4
prime radicalC24×D67D4
cosocleC23×C4×C67C23
hypercenter#1294D67
hypocenterC67C2×#1294
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

1454 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, 59550);